how do you give people the items they buy for fg? you sell it on the market?

Yes through the market place unless you're in the same guild then you can transfer them through your vault.

Make certain that you both are on LS at the same time, and establish communications.

Seller and buyer say 'ready', seller places item on MP, buyer searches MP for item, looking for specifics such as lvl/EE/ str/dex ( 1 or 2 will do), buys item
Once he has item, send T4T.