To start your fishing trip visit the fishing trainer. You can find the fishing trainer in all the capitals and also outside in many places. In the capital you can ask a guard where you can find one.
You will also need:
A fishing rod: You can buy this right next to the fishing trainer. (If you have the silver you a fishing rod with +5 skills is on offer buy this directly with even if you can not use it yet).
Also you should buy 10-20 of Shiny Bauble.
Wow fishing skills 1-50
Now you can start your fishing tour in Durotar or in the forest of Elwynn.
Keep fishing until you reach skill 50. And make sure that you always have your bait active on your fishing rod.
When you reach skill 50, go to the fishing trainer. And buy new lures
The full Guide you can find here