You can simply browse the people who have a game for trade by clicking on the "Users Trading" number in the statistics section of the appropriate game entry. There you can view their profiles and from there see games they have marked as wanted. Next to the number for "Users Trading", there is a [find trade matches] link. It brings you to the Trade Finder, and gives you all the people who have something that you want, if you had marked that game as "Want in Trade".
In order to effectively participate in direct trades, you should mark games you have but are willing to trade as "For Trade" in the "Your collection" section of the game entry. Similarly, you should mark games you want in trade as "Want in Trade" in the same section of their game entry. If you don't have any info saved for a game, then click "Record Info" down at the User Info Section down at the bottom of the game page. Then check the "For Trade" or "Want in Trade" checkbox. You can also do this by searching for the game in the search box. Just click the box under "Status" and a box will pop up for you to edit.
Once you have marked games in this manner, you can use the Trade Finder to identify potential direct matches. If you find a trade you are interested in making, you can send a trade proposal to that user. It is often considerate to send a GeekMail first to your potential trade partner. Checking the "last log in" date of that user can save you some trouble, if you find out they haven't visited BGG for the past 6 months.
You can offer money as a sweetener to trades in the comments, but adding money to even trades out is not supported by BGG.
If you are on another user's profile page, you will see a Propose A Trade With This User with a number in parentheses. The number is that user's overall feedback rating (positives minus negatives). Click the number to see all that user's feedback. If you click "propose trade", you will be taken to a screen where you can set up a direct trade with that person. Games you want of each other's will be bolded and have a background of green. Check the boxes to indicate which games you would be willing to trade for, and which games you would be willing to give up. You can set the number of days that the proposal will be active.
Once you submit the trade proposal, you are entering an agreement with the other party, and if they accept your proposal, you must follow through with the trade.
This is why it is not a good idea to submit multiple trade proposals for the same game at the same time.
Direct trades work fine, but frequently trading can be more effective if multiple parties are involved. For example:
- Person A has game X and wants game Z
- Person B has game Y and wants game X
- Person C has game Z and wants game Y
No direct trades are possible, but if A were to send game X to B, and B were to send game Y to C and C were to send game Z to A, each person would effectively receive a game in trade for one they were willing to trade.
The two most ubiquitous forms of multi-cornered trades on BGG are Ultimate Trades and Math Trades, each of which is described in more detail on their own page.