Is trading between players available in Borderlands?

I just finished a single player session and I found a nice item, for the Soldier class, but I am playing Siren.

I never played co-op till now and I would like to know if it is possible trade items with other human players in some way.

Not through any sort of UI, but you can drop items on the ground. While in a co-op game with a friend, open up the inventory screen, highlight the item, and press Spacebar (or something else if you're talking about non-PC platforms - it will say across the bottom). Your friend can pick it up.

Note that you can't currently trade items among your own characters without routing through a separate player to do so (at least not that I have heard).

I made a trade between my own characters by starting two instances of Borderlands on the same PC. On first I created a new LAN game, on second I connected to it and marked as ready, return back to first and started the game.

It was running quite fine and with some ALT-TABs I was able to exchange items. I'm just not sure how much powerful your PC needs to be to run two instances of the game or if you need an active network interface (thus this may not work when your PC is completely offline).