I think people that do no trading can still have a want list. They want the plants, but none of us can get all the plants we want when we want them, from the vendors we like to use, at the price we can afford, with shipping that seems reasonable...etc.
So we still have plants we want...just in the future.
But, mainly it is like Daniel says, the trading is done mostly by people who have become known to others through their posts and communications. If I am contacted by people I have built up a trust with over time about trading, then we can have a one on one discussion about what is available for trading. For people who have no plant list here on site, who have made few posts, or replies, etc. it is normal to be a little skeptical about what they would be trading. For example: If I have posted pictures of the progress of a plant over the past few years, then it is likely that I actually have that plant, it is things like that that build up confidence in people making them willing to trade. Posting photos, taking part in discussions, showing the plants you received from orders,showing them progressing over the years, are the types of things that build up confidence.
I understand how difficult it can be to trade, I keep a lot of info in my plant list, but do not list any plants as available for trade. I am constantly digging, moving, adding, etc. and not being in the business it is just too much trouble to try and keep and updated running list of plants available for trade. I don't do a lot of trading, but I do some, but I just would not have the time and energy to to be doing all the digging, cleaning, packing, making post office trips etc. it takes when you do a lot of trades.