A lot of the simpler stud finders depend on detecting iron nails or screws used to fasten the sheetrock to studs. Typically these screws are positioned about 12" to 16" or more apart vertically along a stud, and the studs are spaced 16" apart horizontally. So you have to scan the stud finder slowly back and forth, up and down, to find a metal screw. Now, if (as suggested above) the wall covering is plaster over wood lath strips, that makes it more difficult for two reasons. First, the nails used to fasten the wood lath strips to the studs are much smaller than the screws used for sheetrock, so they are harder to find with a magnet. And secondly, those nail heads are topped by a much thicker layer of plaster than the small covering of spackling compound used to hide sheetrock screws. As a fist step to find the stud, try knocking on the wall with your knuckles or a gentle hammer tap. Move your spot sideways and listen to the sound. Usually you can detect a change where the stud is holding the front covering tight. This is not very precise, but it gives you a good area to cover more carefully with the stud finder.
Some of the better stud finders work differently, using a method I don't really understand to detect differences in density of the wall. This is very much like the knocking technique, but more sensitive that the manual way. It does not depend on finding iron nails.
My other technique (our house is old with plaster/ lath walls) leaves more marks. Using the wall knocking process I narrow down the search zone. Then I drill a series of holes, using a long small-diameter bit, horizontally. You can tell when the bit gets through the wall into empty space, versus when it just keeps on drilling into a stud. This way you can know exactly where the stud starts and ends in a horizontal direction. And remember that most studs are on 16" horizontal spacing, so once you find one you have a good idea where the next one is. Afterwards tou need to patch and pain the holes, OR if you arrange it right you do the behind where you're going to mount the picture (or whatever) and just hide them.
As for drilling into wires, that is not usually a problem. The point made above about modern double-insulated tools is correct. You would not get a shock, but the disadvantage is that means you probably would not even know it happened. But the real point is that building codes require that electrical cables be routed through (and along the sides of) studs at the MIDDLE of the vertical wood. So typically the cable is nearly 2" behind the back surface of the wall covering, and you should not be drilling that far in.
I use a very simple and cheap stud finder based on a magnet. But NOT just a simple magnet - you can't really feel the pull with your hand. My device is a plastic thing with a clear cover, and inside is a magnet mounted in a swivelling holder so that the magnet can swing back and forth horizontally. You just watch the magnet as you scan across the wall, and it swings to point to any metal (screw) it passes over.
Of course, you can use other means to fasten something to a wall, depending on how heavy it is. For smaller framed items one of those hangers with a simple nail about 1 to 1½" long pointed down at an angle of about 45 degrees works well. For something heavier, especially when the mount must be somewhere there is no stud, I use those plastic expanding anchors about 1" long that you push into a pre-drilled hole of the right diameter, and then turn in a screw or hook to make it expand and jam against the sides of the hole. For really heavier items I use hollow wall anchors - those things that are about 3" long with "legs" that expand about 1" out right behind the wall's rear surface when you tighten up the long threaded bolt they come with. Once you've done that, the leggy part is permanently mounted in the wall, and you remove the long screw, then use it to mount whatever to that anchor point.