I use a waterproof surveyors fieldbook (Durawrite, Rite-n-the-rain, etc.) And I number the sets with the number they are marked in my GPS with. (and yes, sometimes I forget to use the GPS, in which case I leave the number blank unless I mark them when checking) I leave 3 or 4 lines between sets. I put down date set, type of set, trap used, lure or bait used, and sometimes whether on a drag or staked solid. Then whenever I make a catch I add the date of the catch, what was caught, how it was remade (same trap, different trap, new lure or not, made into a flat set with pile of debris and turds from catch circle, etc.) or if it wasn't. Any time I relure or have to remake the set, such as converting it from a set in dirt to a snow set because it has snow two feet, etc, I note what I did and the date. If I have misses or walk bys I also note that, the date and any information that might be helpful later, such as had a walk by two feet from set and never broke stride, or had interest but the animal circled the trap several times but wouldn't commit, set was worked from side, or back, or set was worked properly with tracks over the pan but due to six inches of frozen snow over the trap it didn't go off.
Basically I note anything that might be helpful when looking back later, so I can see which lures are the most effective, or if a lure might need to age or have smaller amounts used before the animals are confident enough to work it, or if certain sets routinely get worked from the back or side. Or if a location is not as good as I thought, because it has no or few visits in an extended time. Also tells me which traps function best in the most adverse conditions, which ones need repaired after a catch, etc.
Oh, and I only take notes on canine sets, I guess marten sets, water sets, etc. I am confident enough or don't have enough variables, etc. that I don't bother.