Dividers were a mystery to me for a while, but they are a low-tech, elegant way to accomplish very accurate work. I love stuff like that. Here are some different scenarios.
The fundamental task is to divide a length into an arbitrary number of sub-lengths. Let's say you have a board about a foot wide that you want to make nine evenly spaced holes in for a coat rack or game or something. Draw a centerline, and set the dividers for about 1/10th of the distance across the board. Just eyeball it if you want. Then start at one end of the line and walk the dividers along. When you get to the far end, whatever error you made in the setting will mean over or undershooting the end of the board. Say you're about your thumb's width over. Narrow the dividers' setting by about 1/10 of your thumb's width, and step off the line again. It might take two or three tries, but it's pretty easy to get extremely close to perfect, at which point you step down the line again, but this time press as you go to make a clear pinhole mark at each center point. Note that at no point in this do you need to measure anything. The line you're dividing can be any length, and at any angle, although it does need to be a straight line.
Once you've done it a few times, adjusting the dividers to close in on your desired value isn't fiddly. It is trial and error, but you can home in on a very accurate measurement within three or four tries. So don't get stuck in the trap that dividers are some kind of old-school imprecision thing. Let go of your fear, Luke
A common use comes up in laying out dovetails. This can be used for pins or tails (whatever you do first) but here's my tails-first approach. Make a mark a half-pin width in from each end of the board Set you dividers to about what you want a pin plus a tail width to be, and step off down the joint line from one of the half pins. Do a few trials until the last step goes off the board and lands where the far half-pin would end if it were a full pin. It doesn't need to be super exact. Then step off that distance from both ends, pushing in the points to mark out the joint.
Another use is finding the center between two points on a line. This is the simplest case of division (into two). Set the dividers for what looks like the center by eye. Take one step from either end. The mid-point of those two new marks is the center. Widen or narrow the divider setting by half the distance between those points (by eye) and try again. When the points land in the same spot, you have the center.