Pliers, screwdrivers etc. that are used on many types of projects are listed and described under other hand tools.
Fish Tape is a reel of strong, flexible wire that is used to pull new or replacement electrical wire through the walls. If you are dealing with a mobile home with wood paneled walls it may be easier to carefully peal off the paneling, run the wire and then re-install the paneling.
Three prong outlet testers are cheap and simple to use. You simply plug the tester into the outlet and see which of the two yellow and one red lights come on. It will let you identify an open ground, open neutral, open hot, hot ground reverse, hot neutral reverse and correct. In many of these situations everything will appear to work normally and a problem will only occur if someone goes to work on the wiring assuming it is set up properly and it is not. I would use this tester on any outlet I planned to open, even in a new home, just to be sure I didn’t get a nasty surprise. I would be especially concerned in an older home that showed evidence of non-professional electrical work. A multimeter will tell you more about the electrical characteristics of your house, but is probably overkill for most people.
Don’t buy the cheapest wire stripping tool you can find. A good one will strip the wire cleanly and easily and not scratch the wire. Some models have a place to insert stripped wire and shape a loop to go one a terminal.
Voltage detector. A good,cheap way to make sure the wires are dead before you work on them. A lamp or radio works too, if you are working on an outlet.
It is also helpful to have a small assortment of wire nuts and some good electrical tape. Before you go to buy parts, make a detailed plan for your project. Figure out what junction boxes (if any) you will need, any switch or outlet covers (and their color!), etc. It might be useful to draw up a diagram of the project so that you have a convenient reference for sorting through the large array of parts that a supply store will carry.
When using wire nuts, don’t strip too much insulation off the ends of the wires. This can leave conductors exposed at worst. More commonly, fixtures will use stranded wire which can become bunched and knotted in the wire nut. This can have frustrating side effects, such as having a solid conductor fall out after you ‘securely’ tighten the wire nut. After stripping stranded wire, I find that the strands will often untwist. I like to twist them together again to make a stronger piece for inserting into the wire nut. I get better retention when I insert the stranded wire first followed by the solid wire. Doing it the other way makes it more likely that the stranded wire will not connect well because the wire nut will more easily grab onto the solid wire, completely missing the strands of the other wire.