I sing backups and play bass. Sometimes it's hard to hear my singing, and would like a stage monitor so I can hear my voice. I have a spare guitar amp. Can this be used as a vocal monitor? How would I set it up?
You may absolutely use a spare guitar amplifier as your personal vocal monitor.
Set the amp up clean (no Gain higher than 2, and the Bass, Middle, and Treble at 12 o'clock at first) and run the mono cable from your Mix Out (or Monitor Out, depending upon the PA head) jack of the stage PA to the Instrument Input of that amp.
Keep the amp tilted back and pointed at your belly, not your face. You will get the complete PA mix of course, (not just YOUR vocals) but you will hear an approximation of what the audience is hearing.
In-ear monitoring is best, obviously, but if you are gigging tonight, or are in a pinch for spare funds, this will absolutely work.
My covers band did exactly this for a year or so, until I could afford a couple of reasonable monitors. It certainly works, but there are issues.
The most obvious problem is that a guitar amp takes an unbalanced input. Balanced cables and inputs are the only practical way to get the relatively small audio signals over relatively long distances in what's often an electrically-noisy environment. The normal result is mains hum from your amp, which can be at a level where it's obtrusive. If only you can hear it then perhaps you can live with it, but if the mics can hear it too then this is not a good thing.
If you're a small band and you've got the mixer on stage with you, this will probably be tolerable. If you've got a soundman with a desk the other end of the room, you're almost certainly screwed. And if there are old-school incandescent lights with dimmers, you can basically forget it - those things will trash any signal that isn't firmly nailed down.
You also need to have a spare line-out from the mixer. Typically you have separate stage-left and stage-right monitors, so that whoever's stood on each side can have their voice a bit higher in the mix to be able to hear their vocals more clearly. Most mixers have enough outs for this. If you want a third out for yourself though, you may run into problems. A soundman with a desk the other side of the room may well only have two FOH and two monitor feeds back to the stage; and a small mixer you'd have on stage with you might not have enough outs.
Then we get onto the guitar cab. Guitar amps are very directional. As a soundman, I often had to deal with guitarists who turn their amps up to a level which deafens the audience, simply because the amp is pointing into the audience and not angled up at them. You'll need to tilt the amp back so that it's pointing at your head, and you probably want to not move around too much otherwise you might not be able to hear it properly.
And guitar amps have a rather nasty frequency response, even so-called "acoustic" amps. The main purpose of monitors is to hear the pitch though, so you can probably live with that. Just don't be surprised if it sounds a bit like you're singing down a phone, because that's what guitar amps inherently do to any signal.
It's worth remembering that guitar cabs are simply not designed to produce a clean signal. Historically, cheap-ass speakers were bolted any old how into whatever dodgy bit of plywood the Fender company bought cheap that week - but electric guitars happen to benefit from distortion, and crappy speakers mounted in weak plywood frames are a great way to screw over a signal in extremely nonlinear ways. That's why we put mics on guitar cabs instead of just DI'ing everything, because the sound of the cab is an important component of the tone - to the point of course that people go to extreme lengths to recreate the many aspects of guitar-amp-crapness because it's now a characteristic element of the sound we expect. And of course this is everything you don't want in a PA speaker.
If at all possible, using in-ear monitoring has many benefits over using a speaker of any kind. (You can hear it better and you avoid feedback.) Custom in-ears can be expensive, but there are very decent models for under $50. Otherwise... well, yeah, I guess you could use a guitar amp as a stage monitor, if you were on a desert island and had no other options, but it would still be less than ideal (for one thing, guitar amps typically have a very "bright" eq). If you're trying to put the mic signal directly into the amp, with no mixing board involved, then you'd either need an amp with an XLR input or a converter to 1/4 inch (and if your mic needs phantom power, you'll have to provide that somehow too). Just make sure you position it to not "point" directly at the mic—on the floor just behind the mic is common. But really, go for in-ear if possible!