As a level 1 character you should talk with the "Reagents" NPC in the mall. You should purchase "Graccu's Mince Meat Fruitcake" to restore health when necessary. and "Mini Teleporter" (This will be added to your "Pets" collection that's located under your character info (press C to access). Summon your "Mini Teleporter" and travel to "Level Zone". You'll start your leveling journey there, grab some starter gear and get started.

Once you've reached max level you should start doing tier dungeons and weapon zones to get yourself geared up. There's 30 tier instances (16-20, 21-25 and 26-30 is combined). There's also 7 weapon zones (E1 > E2 > X1 > X2 > A1 > A2 > A2 Upgrade). You might need to ask for assistance or group up with other players when you reach the higher tiers.

After you've gotten yourself T30 armor and offset the next step would be to get Top Arena > Ultra Top Arena > Onyxia. You'll start doing Wailing Caverns for the materials needed to upgrade T30 armor to Top Arena > Ultra Top Arena. (It's recommended to get yourself Feign Death to escape the mobs you take with you when running straight to the bosses). Most players will only kill the 3 first bosses( Kresh > Lady Anacondra and Mutanus the Devourer). then reset the instance and repeat. (type '.i u all' to reset the instance in-game. Make sure to be outside of the instance to reset it).

You can purchase Worn Honor Token from the 'Arena Gear' NPC in the mall. It requires you to exchange in 1000 Daily Token and 50 Warsong Mark Of Honor.

You can get Heart of Azeroth by doing the Black Temple questline. It's rewarded from completing part VI from the BT questchain. Onyxia access is granted after completing part XI from the BT questchain.