Get a Multimeter. Preferably with a needle...

If you are at all serious about electronics you probably need to get a multimeter. This is a thing that lets you measure electrical items of various kinds, voltage, current and resistance. I got my first one a very long time ago. In fact, they were quite expensive and I actually ended up buying the bits and putting my own box around the thing. 

Nowadays you can get them very cheaply, and they tend to be digital. They show their readings as numbers. This is fine, but I much prefer one with a needle, like the one above. With a needle it is easy to see if something has just gone up or down. With digits you have to start comparing numbers. Most of the time when I'm testing a circuit I'm really checking to see if something is there or not and I don't really need an accurate value.

I thought you couldn't get cheap multimeters with needles on them, but it turns out I was wrong. You can get the above for less than five pounds from here. So I did. It works well enough and I'm already finding it useful to have around the office.

One important note though. As you can see above the dial has settings that indicate that the meter can read up to 1,000 volts. This is true enough, but you really, and I mean really should not be poking those kinds of probes into signals at that level, on account of a mistake making you suddenly, and electrically, not alive any more. For battery voltages and things like embedded controllers its fine, and it can also measure resistance.  But for high voltages I'd suggest you look at much higher specification tools that will have better insulated cables and probes.