GTS - Its pretty simple, you go to the lady in the upstairs of the Pokemon Center ( Not the one for Wifi or Wireless, but the one for the GTS ) and you choose the GTS.
This is how it works, you basically go in there, and you can request to look at Trades being offered for Any pokeon you've seen in your Pokedex.
Ex. I want a Pidove, I select Pidove. I see trades with people offering Pidove's, and asking for different pokemon in return.
Or you can offer a Pokemon, but you can only ask for Pokemon that you've seen on your pokedex in return.
Ex. I want a Garchomp. And I think a Hydreigon for a Garchomp is an appealing trade to some, So I offer my Hydreigon and ask for a Garchomp.
You can also ask for certain gender's and level's for Pokemon.
This is more simple and care free almost.
You put in what type of pokemon you want and have.
Ex. I have Cool pokemon, and Want Cute pokemon ( Pretty weird )
And it randomly matches you with someone, You then offer pokemon from Your Boxes until you decide on a Fair Trade, and your only means of communication being these dumb looking emoticons.
And thats how the GTS and GTS Negotiations work.