Shamans do not have many quests compared to some classes, but they do have to quest for each of their totems.
Call of Earth
This quest is for your earth totem, and it is first available at level 4. You talk to your trainer and they will send you on the quest.
Troll & Orcs
The quest starts with Canaga Earthcaller, located in the valley of trials. He will ask you to bring two Felstalker hooves to him. These drop from the felstalkers inside of the northern cave. He gives you an Earth Sapta. Go to the hidden path located around 41,73. Follow it to 44,76, once there, drink the Earth Sapta and talk to the earth elemental that you see. He will give you a rock to return to Canaga. You will then receive your first totem.
Tauren
You quest starts with Seer Ravenfeather located at camp Narache. You will be sent to gather two ritual salves that drop off the bristleback shamans. You will be given an Earth Sapta that you need to drink at the Kodo rock located at 53,80. You will then see an earth elemental that you need to talk to. Take the stone back to Seer Ravenfeather, and you will get your earth totem.

Draenei
Your quest begins with Firmanvaar. He gives you the quest to Spirit of the Vale located at 72.0, 40.6. Talk to the Spirit of Vale and he asks you to kill 4 restless spirits of earth. After killing these, Spirit of the Vale will give you a stone to return to Firmanvaar. Firmanvaar will then give you your earth totem.
Call of Fire
This quest can be started at level 10. This is to obtain your fire totem.
Horde
You start this quest by talking to your class trainer in your major city. You are told to seek out Kranal Fiss. Kranal Fiss is located at 56,20 in The Barrens. Kranal will send you to find Telf Joolam who is in Durotar. The path up to Telf can be hard to find, it is around 36.5, 57.0. You should see a black rock marking the way up to him. Telf will send you to gather Fire Tar, and a Regent pouch. The Fire tar drops off the razormane casters in The Barrens located east of Crossroads. The Regent puch is dropped by Burning Blade Cultists located in Durotar in side a cave at 52, 29. After getting both of these, run back to Telf. He will give you a Fire Sapta. After drinking the Sapta, you go up the trail a little farther to see an fire elemental; kill him, and then place the glowing ember you loot in the brazier, then light your torch and return with the Torch of the eternal flame to Kranal Fiss.
Alliance
Sulaa in Exodar will send you to speak with Tuluun in Azure Watch. Tuluun will then send you north to approximately 59,17 to talk to the fire spirit named Temper. Temper will send you to the west to kill Crazed Wildkin to find a Ritual Torch. Return to Temper with the torch. You then need to run to 11,82 approximately. Kill the surrounding owlbeasts, and then use the torch to light the effigy. Kill Hauteur and take his ashes back to Temper. Use the orb Temper gives you to port directly to him. Temper will send you back to Tuluun. Tuluun will then send you to Prophet Velen in Exodar. Prophet Velen will then give you your fire totem.

Call of Water
This is the quest for the water totem. You can first get it at level 20.
Horde
You get this quest from your major cities shaman trainer. You will be sent to find Islen Waterseer in The Barrens. Islen is located just south east of Ratchet off just off the shore. Her coordinates are aproximitly 65.8, 43.8. Islen will send you to find Brine. Brine is located in southernThe Barrens at 43.4, 77. 4. Brine's first task is to simply fill the waterskin she gives you with water from the pool at the base of the hill she is on. The next step is to fill a waterskin with water from Tauren Mills in Hillsbrad. This is a long run. Once done bring it back to Brine. Brine now wants another waterskin filled from a shrine in Ashenvale. The shrine is located around 33,67. It is surrounded by water elementals. Just take your time killing them and then fill the waterskin. Brine will then send you back to Islen with a Vial of purest water. Islen will give you a Water Spata. Take the Water Spata and head to Silverpine forest. Go to The Sepulcher. You can find a way through the mountains behind it to the shrine located at 38,44. Once at the shrine drink the Spata and kill the water elemental that is there. Take the bracer and put it on the shrine. Follow that up with using the vial of purest water on the bracer. Make sure you wait and talk to the elemental that appears. Take the Shard of water and head back to Islen. She will give you your long sought after water totem.
Alliance

Your trainer should tell you to seek out Farseer Nobundo in The Exodar. Nobundo send you to find Aqueous. Aqueous is located off the north coast of Bloodmyst Isle at 31.7, 16.1. Once you get to the location dive straight down. You can use the water potion that was given to you or you can dive right down and use the fissure that is right next to Aqueous to breathe. Aqueous wants to you travel south west to the foul pool and kill Fouled Water Spirits until you have six Foul Essence. Aqueous wants you to now fill a bota bag with water from a well in Ashenvale. The shrine is located at 33, 67. It is surrounded by water elementals that you need to be careful killing. They are all around level 23 and can be hard to kill sometimes. Once your bag is filled head back to Aqueous. Now you need to go kill Tel'athion the Impure. To get Tel'athion to spawn you need to use the water on the barrels at 25.6, 41. This will bring Tel'athion out, it will also spawn some water elementals who will help you kill him. He is a caster and

is a pretty quick kill with the elemental help. Return to Aqueous with his head. Aqueous is done with you and will send you back to Farseer Nobundo. Farseer Nobundo will reward you with your water totem.
Call of Air
This is your final totem quest. You can start it at level 30.
Horde
The quest starts with the shaman trainer Searn Firewarder in Orgrimmar, inside Thrall's chambers. Searn will send you to find Prate Cloudseer in 1k Needles. In 1k Needles go to aproximitly 54, 44 and you should see a path up to a cave on the side wall. Inside you will find Prate Cloudseer. Talk to Prate and she will give you your Air totem. Yes, it is that simple.
Alliance
You have to talk to Farseer Nobundo after talking to your other alliance trainer. Nobundo will send you to talk to Velaada who is just north of Exodar. Take the path that starts at 26,26 to get to Velaada. Velaada has you talk to the air elemental outside her cave called Susurrus. Susurrus gives you a Whorl of air to bring back to Nobundo in Exodar. Give Nobundo the Whorl and he will give you your air totem.