I do it a few ways...I'll send out offers through the site occassionally but more often (after the first few weeks generally) I'll send out some feeler emails..."looking to do anything?" "I'm looking for a wr, interested in dealing any of your guys?", "looks like your banged up at wr, interested in any of my guys?" for teams weak/strong in certain positions. I like to throw out positional inquiries because if you ask about a certain player sometimes an owners radar goes up. So if you can keep it generic you may get the guy to offer up the player your looking for and get him cheaper than if you asked for that specific player. It will also show the owners pecking order in how they feel about certain players if you probe a bit.
Generally, I'll target certain players I'd like to get and have certain guys that I'll be looking to move. I'll ask if a particular team is interested in one of my players and kind of take it from there. I think a dialogue is always good because you can get a feel for how a feels about a certain player, if he loves him (and I'm wasting my time) or is taking a wait and see approach. If it's the later you can keep it in the back of your mind and monitor the situation and then may have a chance to pounce if they run into a string of bad games, injuries, bye week problems, etc.. If you just send out and offer through the site, they reject it and you get no feed back or information on what they really feel about a player.
Often times what starts out as a meaningless dialogue early in the season will end up resulting in a trade later in the season.