We receive our first mount at level 40. It is gotten by talking to a warlock trainer in a major city, travelling to Ratchet, and speaking to Strahan Farsan. He will give you the spell to summon the Nightmare, no questions asked. He hints toward there being effort involved to get in in the future, so Blizzard may add a quest later. For now, its all free.
The dreadsteed, our level 60 epic mount, is a different matter. Before I lay out what you need to do in the quest, let me list what you will need, in total, to bring this to a good end.
Requirements
Beside having to be level 60 to start actually the quest, you can start gathering materials used in the quest sooner then that. This is what you need;
406 gold, or 156 gold if you know a warlock with the items for the summoning of the dreadsteed event.*
25x Dark Iron Ore - If you are a miner, or have a friend who is, you can get this in Burning Steppes, Searing Gorge and Blackrock Depths. It can also be mined in Molten Core, but that zone isn't visited by many guilds these days. Lastly, it is also frequently up in the Auction House.
(I'm leaving prices out, as they are different for each server, and change alot as time passes)
6x Large Brilliant Shard - Either an enchanter or the Auction House will provide these for you.
35x Black Dragonscale - These are skinned. Find a skinner or use the Auction house.
10x Elixir of Shadow Power - Herbalism / Alchemy. These elixirs take 3 ghost mushrooms to make. I don't see the elixirs themselves in the AH much, so if you want to buy them, it might be easier to get the mushrooms instead.
3x Arcanite Bar - Mining. Arcane Crystals are a rare find out of Rich Thorium Veins. Coupled with a thorium bar, an Alchemist can turn one into an Arcanite Bar. That transmute spell is on a 2 day cooldown, so expect to pay for that too.
Note that you can do the prequests (collecting the ingredients and gaining access to a vendorbought item in jaedenar for 150g) without spending more then 6 gold, excluding anything you might pay for the ingredients.
*At the second to last step of the quest you have to buy some items from a goblin vendor. They costs 250g total. However, at least as the situation is currently, you retain these items after completing the quest. It is

possible to initiate the event for fellow warlocks, without them having to buy the items as well. You can also do the final event with more than one warlock in your group, all will be able to complete it. You can even summon someone in after doing the event.
Step 1: Starting the quest
You receive the quest at 60 from your local warlock trainer (major cities only). Speak to one, and you will be sent to speak with Mor'zul Bloodbringer in the Burning Steppes. He is located in a small encampment just west of the Altar of Storms, which is in the northwest corner of the zone.
This quest has a sidequest you can do before or after the main quest. You can get the quest from the goblin, its walkthrough is shown a bit further down this guide under the title 'Xorothian Stardust'. You’ll need 150g to finish this sidequest, but can do all the work leading up to the 150g step in advance.
Mor'zul’s quest is to gather blood from Owlbeasts in Winterspring.
Unlike the quest text may seem to suggest, you can kill any type of owlbear in winterspring, they can all drop the blood.
I estimate the droprate to be about 20 - 25%.
The greatest concentrations of Owlbeasts are found to the northeast of Everlook, as well as to the south, roughly between Everlook and Darkwhisper Gorge, in encampments to the east and west of the road. You can also find some wandering owls in the west of the zone, to the north and south of the road.
They are all easily solo'd, but bringing a friend or two to help you will speed things up.
When you turn in the owlbear blood, (and give it to the goblin, then speak to Mor'Zul again) you are presented with three followup quests.
1: Wheel of the Black March:
Collect 6 large brilliant shards and 25 dark iron ore.
2: Bell of Dethmoora:
Collect 10 elixirs of shadow power.
3: Doomsday Candle:
Collect 3 black dragonscales.
After turning in all of these, you will need to turn in 3 arcanite bars.
Once you have collected and turned this all in, you have two steps left to take before reaching the final quest, unless you have already done the sidequest shown below.

Xorothian Stardust
The last item you need is Xorothian Stardust. The goblin makes mention of it, and sends you off to speak with Lord Banehollow in Jaedenar, Felwood. Before you take off though, You'll need to buy a set of his potions. (Cost: 6g)
Jaedenar lies directly southwest of the Bloodvenom Falls. Drink a potion, and you can make your way through most of the cave without aggro. There are goos about halfway through, but they can all be avoided by some creative jumping and walking.
It can be easy to forget that you aren't in an instance, and can still run away from enemies in here without having them chase you forever. Keep that in mind if you end up with multiple goo's trying to dissolve you.
Lord Banehollow is a dreadlord at the very end of the dungeon.
Banehollow has a task for you, which is to kill his traiterous underling Ulathek. Head back the way you came. Once you've passed through the room containing a named warlock and 2 named succubus underlings, look for a small bridge leading into a small room with two orc defenders in front of it. This is Ulatheks spot.
After speaking to Ulathek, both he, the orc in the room with him, and the guards outside will forget about your shadowy potion effect and turn hostile.
Note: only these four mobs turn hostile, the rest of the demons in Jaedenar remain friendly while you're under the effect of the potion.
It may be possible to avoid aggro from the guards outside. When I did the quest I wasn’t in the best spot for avoiding aggro, so all four aggrod on me right away. Still, it wasn't a lost cause at all. Using voidwalker's AE taunt or Howl of Terror to keep the adds busy, you can quickly dispatch Ulathek and loot his head. After that, simply running away will eventually make the other orcs deaggro and return to spawn.
Return to Lord Banehollow and turn over the heart. He will tell you to see his servant Ur'dan for Xorothian Stardust, who is standing beside him.
Cost: 150g
Scholomance
When you give the stardust to Gorzeeki, he has another task for you. He needs you to travel to Scholomance and use the imp in a jar he gives you at the alchemy lab there.

Take note that Scholomance is meant for a full group of level 60’s. Not many people go to Scholomance anymore, and it may be difficult to complete this step. If you can't get a group for it, try to find a group already in the zone (/who scholo) and see if they will let you complete the quest when they're finished with the zone.
The lab is located in Ras Frostwhisper the Lich’s room. As you enter his room, it’s immediately to your right. You can recognize it by the two large kettles hanging from the ceiling. At the lab, use the imp in a jar. He jumps around a little, and thats that. No enemies spawn, nothing dangerous happens.
That’s saved for the last step.
The Final Step: Dire Maul
Now that you've finished the quest in scholomance, its time for your last visit to the npc's in Burning Steppes. Give the imp to the goblin, and speak to Mor'Zul again. He will give you the final quest. It comes with a book of instructions for the final event.
You are told to buy three items from the goblin. J'eevee's Jar, A Black Lodestone, and Xorothian Glyphs. You are not required to the items. Instead, you may know a warlock that already has these items, and can trigger the event for you. You will receive quest credit in this case. Per Blizzard, this is intended to function like this.
If you do choose to buy them, you get to keep these items after finishing the final event. They cannot be sold back to a vendor, but they can be used to initiate the event again.
Before you can begin the event, you will have to do a regular clearing of the Dire Maul west wing. As with the scholomance, it can be difficult to find a group for this. If you've got a few high level friends willing to help, this instance can be done without a full group.
Make sure you bring a lot of soul shards, you will need them for the event.
Heres a short walkthrough to Dire Maul west:
You need to enter the instance through a door in the west of the Dire Maul area. To do that, you can obtain a Crescent Key by doing the imp event in the eastern instance, or use a rogue or seaforium charge to pass through the door in the west instance. You can also die on one side of the door, run back and resurrect on the other side, then open the door for the rest of the group using the torch on the inside.

Inside the instance, you will find large crystals (pylons) surrounded by elementals. there are 5 pylons in total, and all elementals around them must die to open up Immol'Thar's prison at the end of the zone.

One pylon is near the entry, can't miss it. Two pylons are upstairs. Cast detect invisibility on your party, as there are some invisible undead roaming around these areas.
The last two pylons are downstairs, past a big named tree and through a tunnel.As you clear the last pylon, the large blue shield around the big circular area in the center will fade, and you can enter it to fight Immol'Thar.
Once Immol'Thar is dead, you can initiate your quest event. Make sure everyone is ready for a hectic 10 minutes.
When you release the imp from the jar, he will place three artifacts around the circle.The three artifacts provide you with powerful buffs. Every so often, one of them will fail. They make a sound and begin to float a little lower than they were before. It is critical that you run up to them and rightclick them the moment this happens. Doing this costs a shard. I use about 10-15 during this event. Note that you, or whoever triggered the event for you, has to have the Black Lodestone with them to reactivate the artifacts.
With all the artifacts in place, the event starts. Imps begin to spawn and charge your group. The most essential thing here is to keep checking the artifacts to see if any are powered down, its easy to miss it. The imps themselves are nothing to be worried about, the doomsday candle will deal enough damage to kill them over time. It is important that the person that keeps the artifacts up and running isnt being hit by the imps, as melee damage interrupts the reactivation of the artifacts.
After a few imp waves, a Dread Guard will spawn. They can be enslaved and banished. They can’t be feared. Enslaving the first one (or more if you're grouped with other warlocks) to kill the rest makes this fight alot easier. The imps keep on spawning, and the dreadlords slowly keep adding as well. If you can survive this for about 6 minutes, you will win. You can check how far along you are by seeing how far many runes are visible around the circle. If they’re all there, you’re done.
You can now summon the Dreadsteed. It's a typical bossfight, and not very hard. After a short time of fighting it, its master spawns as well, a Dreadlord. He's not very hard, and you can carry on fighting the Dreadsteed, killing the master afterwards.
This event is actually one of the most fun one group events I've done in WoW before the Burning Crusade was released.
When the Dreadsteed is dead, you can talk to its spirit, and will receive what you've been working for, the summon Dreadsteed spell!
Enjoy the speedy travels :)