This seems really stupid, but I can't, for the life of me, figure out how to pay my riders. I've just been going and changing the date they get paid to the current one so that they get paid and I can start training. I know this makes me pay them for 2 weeks of pay, though. How do you pay individual riders?

All of your riders are already paid. When they need to be paid, go to Stable > Riders Lounge. Any riders whose mood is in red needs to be paid.

To pay a single rider, click on their name in the Riders Lounge to go their page. At the bottom, if they need to be paid, there will be a Pay Rider Submit button.