Just about any cheapie multimeter (often called a voltmeter) will do the job. If you have a Harbor Freight nearby, they usually have a couple for under $10. Otherwise just about any meter you find at Walmart, a car parts place, Tractor Supply, Radio Shack, etc will do the job. Make sure it has a DC volts scale greater than 12v. Also an ampere capability (200 milliamp and 10 amp scales are typical) is useful for finding small current leaks. You do want a meter with leads (wires) and preferably leads with alligator clips (clip them on to free up a hand).
The main caution using a meter involves the ampere scale. If you were, for example to connect the meter across the battery in current mode (amp scale) you WILL damage the meter. If you are lucky it will only blow an internal fuse inside the meter. So be sure you are in a Volt scale when you try to measure volts.