Not to be snarky, but have you read the manual? That's a good place to start.

Yeah I read it pretty thoroughly, but I still don't understand all I've learned. For example, I see that I can connect powered speakers to the stereo L/R jacks, but I don't know where to run a line to the amp for the subs. I see that there is a L/R for monitors, but three of the guys in the band have in ear monitors, and two of us use regular floor monitors. I don't know where to run a line to the amp for those floor monitors either. I'm trying to learn from actual people instead of a manual.

It would kind of help us help you if we know what gear you're interfacing with...
Are the subs "active"? This means that their power amp (and crossover processing) is built into them.
If not, they are "passive", and need an external power amp to run them. In this case, you will need an "active crossover"
to split the sub range from the "house" systems, plus a power amp to drive the speakers.
Are the house speakers "active" or "passive"?
That little mixer can't provide you with too many monitor mixes, you can use the "Aux" sends - 1 & 2 - to feed an IEM mix and a Floor mix with their pre/post switches set to P R E . This means that the channel faders will not disturb the monitor mixes. If you have those set to "post", the faders will affect the level to the monitors as well. You want to make sure that the channel faders do NOT affect the monitor mixes! Then, of course, you have the Effects control, which is essentially a "post-fader" mix, to the internal effects unit. Don't do what many amateur sound mixers do and overuse these effects. This is icing on the cake. Learn to get a clear mix without overloading the mixer. More on this later. Now report back with what you're going to be using...

Ok, the subs are not powered, but the mains are. I'm not sure of the brands and model numbers, but I can get that info if it will help you give me a more thorough answer, and if you're patient enough and willing, I would be greatly honored.

We have two power amps and a crossover, and, again, I have no info on them, but the guys have been using the whole set-up for a PA for a while before I joined the band. The only thing different about it now is the new Yamaha board.

I think I had figured that out about running cables from the board to the crossover and then to the amps, then out to the speakers, but I'm really not sure if I would know where to make all the connections if I actually got in the rack to hook it all up.

That's very helpful info on the monitor thing. I will do just as you have said. And thanks for the reminder about the effects. If there's one thing I DO know about all this, it's that no effects setting is going to make miracles. I always try to get the cleanest, clearest signal possible.