Hello @[mention]dln30[/mention],
In order to trade evolve, you must have at least one free slot in your team before the trade:
If you have 6 Pokémons, and trade 1 in return of the one you want to evolve, it will go into your PC, assuming your team is still full, even though you would technically have 5 + the traded one.
When doing so, you will receive the traded 'mon in your party, and the evolution request will appear. :)
Also, please note that you can only evolve one pokémon at a time, meaning that you have to trade as many times as you have Pokémons to trade evolve :Angel:
Enjoy your new 'mons! :D