If you are building the electronic guts of many robots, you will often need to test circuit function and component values.

Having, and knowing how to use a multimeter is an invaluable skill. The first peice of advice I will offer any new robot builders is to buy a Digital one. Analog ones are awkward to read, not very precise, and to be frank a bit obsolete.

Entry level multimeters should cost no more than around £15 (less if you really look around at computer markets). They should also come with one set of probes - though eventually you might think about getting others. Also consider how many digits it will display - again- for entry level, four should be sufficient. If a manufacturer specifies 3.5 - they mean the first digit can only display a 1.

Most multimeters have enough functionality to read resistance, current and voltage.

Since resistors are one of the most common components you are working with - you will regularly use this one. All the settings marked with the Ohm Symbol & are resistor markings. There are a set of different resistor value ranges, so you try and go with the nearest one - or start low. If you test the resistance, and see NO or 1, try shifting up to a higher setting. Most go from 1Ω (on the 2Ω setting) up to 2MΩ - this is a very high resistance, and although I have seen them, it is very rare you will use a resistor over this rating. For each setting- you are able to measure resistances less than, or equal to it. Some meters are “Auto-Ranging” - so you do not have to select a setting. Even if you are familiar with the resistor colour bands, I often check the resistance anyway, because some resistors (especially if salvaged) may be damaged and offer a much higher, or lower one than printed. If you are totally trusting of the colour bands, and do not check - you may find you have to desolder a dud.

The next tool you will regularly use is continuity checking. It is often very worthwhile knowing if a circuit, or cable is clear-flowing and not broken. On some multimeters- you will have a specific setting, and an LED or Tone which sounds when the check is successful. On others- many of the entry-level ones, you can use the diode test functionality.

Digital Multimeter With Backlight Draper You might not use the backlight much but there will definately be situations where you will have wondered how you did without it. I prefer this rotary kind of MultiMeter. Ensure you buy a digital one like this as the analogue ones really do not live up to what a roboticist will require. It is cheaper from Amazon than many local tool shops - and has all of the beginner functions for measuring resistance, current and voltage. It also has Diode and Transistor testing.
Getting the Most from Your Multimeter... R.A. Penfold If you are serious about using a multimeter- or interested in using one for more purposes - this is a great little book - at less than a fiver, why not. OrionRobots has a collection of the R.A. Penfold books - which while small, come highly recommended.
Junkbots, Bugbots and Bots on Wheels: Building Simple Robots with BEAM Technology Dave Hrynkiw, Mark W. Tilden I recommend this book again - as it has a neat little section on using a multimeter and other electronic stuff. Since you can build robots with it as well - you should probably have this in your library.