Putting points into each of the talents trees will generally improve that trees area of expertise. As a mage you will usually be focusing on either arcane, fire or frost damage. SO you will want to focus on the tree that will increase that. But it usually isn't wise to put all your points into one tree. Putting every point in fire will give you huge fire damage. But if you also put a few in arcane so you get Arcane Concentration or some in frost so you get Elemental Precision you will have just as much damage and improve your performance in other areas. While many people try to go as far down into a tree as they can there is also a balancing game of going as deeply as you can into the other trees. This juggling of talents has led to the rise of Builds. Tested patterns of talents that players have found are the most effective at increasing one or more styles of play. But in the end, the skill of the player determines a characters success more then their build.

PVE Builds
Arcane/Fire PVE build.
Arcane is generally not a good source of damage for PVE because of its high mana cost. Usually you will use it as a support for fire or frost damage, while keeping most of your points in the arcane tree. This is the one of the heaviest arcane builds you can use without wasting points on bad talents.

Arcane/Fire Build 2
This is very similar to the build above, but you will be using a mix of arcane spells like arcane blast and missiles, and fire spells like fireball and scorch instead of just arcane damage.

Arcane Frost
I personally don't care for arcane frost that much because so much of the good talents in the frost tree are far down, and frost is much weaker compared to fire unless fully buffed. You will be able to pull off huge crits with Spellpower/Ice Shards and have more control over opponents than arcane/fire. But since it relies on shatter and freeze you won't find it very useful in raids or most groups where mobs are immune.

Deep Fire
This build will give you some of the highest PVE damage potential you can get, while maintaining sustainability. On the downside, it has very limited survivability so I recommend using it in groups and raids where you will have support protecting you. The majority of your damage will be coming from fire spells, especially fireball. You will rarely use arcane or frost spells and you only put points in these two trees to help enhance your fire damage. The build given below has three points left which you can spend depending on what you will be playing. If you are doing five man content and below Blast Wave and Dragon's Breath good choices, especially in outdoor areas. But if you planing on fighting elites three points in improved fire blast would be a better choice.

Light Fire /Arcane
This is a trimmed down version of the fire build above with more attention paid to the aspects of raiding. The fire tree is gutted of all the none powerful talents so you can put more points in arcane for greater mana efficiency. Your arcane spells will also be more potent, but you will only really be using arcane explosion for AOE. If your gear has enough spell hit you can take one point out of Elemental Precision and put one more in Arcane Meditation.

Fire Frost Elementist
This is a hybrid build where you will be relying on your fire spells for damage, and your frost spells for control and support. I find this personally best for solo play and farming, but it is also good for fiveman content and ten man raids.

PVE Frost
This is in the same vein as the fire arcane build but uses frost instead of fire. You will be relying nearly one hundred percent on your frost spells for damage. Frost is very strong as a PVP tree, but suffers a little in the PVE department unless you are playing solo. Most mobs in instances and raids will be immune to freeze or chill effects, which are the key to frost DPS. It's still an effective DPS build though and makes an excellent grinding build.