In the above example you will see the subject of this thread is 50 FP. The different thread titles denote the amount which you are swapping with your guildmates. If it's a 5FP swap it's 5 FP 10 is 10 20 is 20 and so on.
When you post you put 50 FP on Player A's Arc, when Player B posts they put 50 Points on your Traz. The next person to post will put 50 points on Player B's Chateau. All you post is the name of the GB you want your points on, then fulfill the swap with the person above you.
The only other things you may see posted in a swap thread is either something like Arc-thank you/please which is just someone being polite. Or Arc 416, the 416 denotes the amount that is currently on the arc and is just that person keeping trade of their points/making sure their swaps are being fulfilled correctly. In either case you do the same thing, post the name of the GB you want your points on and put the points on the building they have named above. The person who posts after you is responsable for putting the points on yours.
A private swap does not get handled on the swap threads. Whatever arrangement you and another person have come to can have whatever terms you agree to. One way of keeping track is to have a private thread open with that person where you log your contributions.
Me and this guildmate trade 50 points per day so every day we post to each other. Other ways you could go about this is instead of a fixed amount per day you trade a set amount over time, say 300/week. To do that you would keep a similar thread with that person and post the contribution you have added out of how many points to keep trade. IE I put on 20 points in the morning I would write +20 20/300 then 50 in the evening I would post +50 70/300.