This guide is written from Alliance POV, I will try and create a Horde POV guide soon.
Note: All tournament quests appear under the “Tournament” category in your Questlog.
Head north into Icecrown, to the Tournament’s Starting Area (69,2 and inside the building here to speak to Justicar Mariel Trueheart. Accept from her “The Blastbolt Brothers” and “The Argent Tournament”
When this is done turn in the Blastbolt Brothers (A goblin near the south end of the Tournament staging area) which is located at (75,24)
Turn in “The Blastbolt Brothers” at this location and then accept from the two goblins “Jack Me Some Lumber” and “A Chip Off The Ulduar Block”.
Next step is to fly over to your faction tent, which is North East of here for Alliance over at 76,20. Head inside and turn in “The Argent Tournament” to Arcanist Taelis, accept "Mastery Of Melee" from him and “Mastery Of The Shield-Breaker” and “Mastery of The Charge” from the other two questgivers located next to him.
In your bags equip the [Alliance Lance] and head outside of the building, on your left is a horse, jump on it and head north west towards t he training dummys.
At 73,19 ask Valis Windchaser how to train with a ranged target, some instructions will appear in your chatlog which explains what to do, simply target a ranged target and spam the 2 button until your quest is completed, its simple!
Next at 72,19 speak to Rugan Steelbelly and ask how to train with a charge target, again instructions will appear in your chat window which shows you what to do. Target a Charge Dummy from range and press 2 then 3 when its off cooldown, rinse and repeat this twice to complete the quest.
Finally at 72,19 speak with Jeran Lockwood and ask how to train with a Thrust Target. Then target the nearby Thrust dummy and hit 4 then when in melee range press 1 to thrust the target. Do this 5 times and the quest is done, if you get low on health wait a few seconds until your out of combat, then press 5 to fully heal your mount.
Now you are ready to go back and hand in the quests, head back to the alliance building at 76,20 and hand in these three quests to the associated questgivers. When you’ve handed them in 4 more quests will unlock, accept them “The Edge of Winter”, “Up To The Challenge”, “Learning The Reins” and “Training in the field”.
Go out of the building, mount up on a horse again and head back to the training dummies at 72,19. Do the same as you did a moment ago on these dummies individually and complete the quest objectives, then you can go back and hand them in.
Now head out of the building and into storm peaks to around the engine of the creators and the ridge between ulduar and the mainland. All around here (37,40) are small blocks of stone sticking out of the ground that you need to blow up by standing next to and using your Goblin Chisel, i suggest running away from the explosion to avoid taking unnecessary damage from, keep doing this until you have all 15 pieces picked up off the floor from the explosion.
When you have all 15 Small Stone Blocks head south into Crystalsong forest to the great tree around 15,35 and find the friendly trees (real trees not tree-ents) and use your axe on them, when you’ve used the axe you’ll get 2 pieces of wood and an Angry Oak Spirit attacking you, kill the Spirit then move on to the next tree until you have all 12 of the Rough Hewn Planks.
Once this is done head to 53,72 to kill Lord Everblaze here up on the platform next to the dome building. Now for the next part of this quest, head to Howling Fjord to the lake at 42,19 to the NPC here, use your Everburning ember you receive from Lord Everblaze on Maiden Of Winter’s Breath Lake to receive the final item in this quest.
Now for the return leg back to The Argent Tournament, head back into Icecrown to Sindragosa’s Fall at 75,42 and kill any 8 of the mobs around here you see, they all count towards the quest “Training In The Field”
When this is done head back to the argent tournament to your goblin quest givers at 75,24 and hand in the two quests here, finally head back into the alliance building at 76,20 and hand in the remaining two quests you have.
Now time to head back to the visiting area over at 69,28 and pick up the next quest, “The Black Knight of Westfall?” This involves going to westfall, quite a trek so I hope you didn’t blow your HS CD earlier getting back here. Pick up th e quest and head to Dalaran, through a portal to Stormwind and fly to Westfall. From here head to 40,69, the book is inside the house next to the barn adjacent to the summoning stone for Deadmines.
Now use your hearthstone and fly back to the visiting area in Icecrown to 69,28 and turn in the quest “The Black Knight of Westfall?”, then accept “The Seers Crystal”
The next part of this quest takes us to Crsytalsong Forest, go south into there now 47,40 to kill Unbound Seers for an item [Seers Crystal]. Unbound Seers are like Satyr and should be fairly easy to spot in the Ruins. Anyway when you have the Crystal head back to the visitors entrance at 69,28 in Icecrown and hand in the quest.
Accept the quest “The Stories Dead Men Tell” and head east to the graveyard on the opposite end of the Tournament at 79,22 and click on each of the sparkling graves here, this will complete the quest; now head back to the visitors area at 69,28 in Icecrown
Hand in the quest and accept the next part “There's Something About the Squire”, time to head back to Crystalsong Forest, to 38,60 to kill some Skeletal Woodcutters around Maloric until you get the Femur, then go to behind Maloric and use the Femur to sap him and take his Toolkit by clicking on him, now time to head back to The Argent Tournament Visitors Area at 69,28, turn in the quest inside.
Pick up the next part in this quest “The Black Knight’s Orders” and fly over to the small tent located at 78,22. Click on your Enchanted Bridle next to the Gryphon and be taken to the next location. Fight your way up the hill killing all the cultists and inside the building at the back are the two quest items you need to complete the quest, when you’ve got them fly back to the visitors area at 69,28 to hand the quest in.
In the hut at 76,19 you may have a new daily, “A Worthy Weapon” if you do it’s a fairly simple quest, head south into Crystalsong to around the edge of the lake near the dam which flows from Icecrown, Hyacinth grows all along the cliff edge of the dam (72,74) in Icecrown). Collect four of them and head to Dragonblight 93,26, just East of Light’s Trust in the water. Use your bundle of flowers here and pick up the weapon in the lake. Quest done! Head back to the hut at 76,19 in Icecrown and hand it in.
I will update this guide with any more information I gather from participating in the tournament, hope you found this guide useful.