Question - how do Steamtrades.com works exactly

Exchange table ? I don't think such a thing exists.

Normally you decide who goes first for example by comparing Trade rep and then that person goes first and has to trust the other person will go through with the trade as well.

Is that what you wanted to know ?

It is a bargain market forum. People post threads of what they have to sell or what they want, and other can reply on it. Then they add each other as friends on Steam, work out the details in chat (which the smarter ones screen cap all the time), and then do the trade.

Most often lower trade rep user posts their stuff first. It is a fairly common occurrence (although when I traded, I largely did not care).