At my first barn, I paid after the fact for lessons on a monthly basis. I also worked at that barn regularly because I was flat broke, so the amount I owed each month was very different, sometimes by hundreds of dollars. I kept a running tally myself, but I can't for the life of me remember how they let me know how much I owed. I think it was verbal, honestly. Everything at that barn was verbal, which is amazing considering it was the tightest-run barn I've ever been at.
Barn #2 I only paid two months of board, one of those a sacrifice month due to leaving without notice, so that doesn't count.
Barn #3 was precisely the same base amount each month. There were no extras. I used an outside farrier, a different vet, and never lessoned with the barn's trainer. When I took lessons it was with an outside instructor and I paid that person directly.
Barn #4 was also precisely the same amount each month, and it included four lessons per month, as required. I am still really torn on that system. On the one hand, it was terrific to have a guaranteed weekly lesson, and I really improved quite a lot under that system. On the other hand, my schedule could be unpredictable, and when I missed a lesson it wasn't easy to make up. When Tristan was off for so long, I did some lessoning on other horses, but not consistently. I built up a HUGE bank of lessons that was basically money left on the table, which was hard.
My current barn does it my very favorite way: they invoice me. It sounds so sensible and business-like that I'm amazed I've never seen it before!
F'rexample, here's my July board bill. It's all itemized out: fecal samples, the farrier visit, and the basic board. When I work off lessons, that's accounted for, as are lessons or training rides or other services. They're also dated, so when I file these I have a really good records system. I love it. I also love that the barn covers the farrier and bills me monthly. It baffles me, I have to be honest, but I do like it. It eliminates one of the "did you leave a check?" conversations each month.
Every barn I've ever been at I've paid by check, though. If I could pay by credit card, that would be truly living the dream. I would love to add the points to my stash, especially right now since I'm saving up for the honeymoon in travel points.