Go to the GTS in Goldenrod City. You will need a Wi- Fi connection to your console
You can Seek Pokemon, or you can Deposit Pokemon.
Seeking Pokemon is where you can see all the people that have put up a specific Pokemon up for trade. You have to ask for a species, but you can also narrow down the results with a specific gender, level etc..
Depositing Pokemon is when you can put up a Pokemon of your choice up for grabs, for another Pokemon of your choice.
There are no negotiations in the Generation VI GTS. Unfortunately, only in the Gen V one.
Hope I helped. :)
Source: I use it a lot. :P
