Well, the answer depends on the robot. If your robot comes as a kit, you might not need any additional tools at all, or only those supplied with the kit (such as an Allen wrench or a Phillips head screwdriver). If you're building your own bespoke robot you may need to construct your own chassis or hardware components, or ask someone with tools and experience to help you. It's important to learn how to use both hand and power tools properly — they can be quite dangerous if you don't know what you're doing or if you don't use sensible practices such as clamping your materials properly before drilling or cutting (I have a few scars to prove it).
Buy as good a quality as you can afford: good tools can last your lifetime if you take care of them (don't leave them somewhere they'll rust). I have a pair of scissors from 1978 and they're still sharp. My pliers and cutters are still like new and I use them a lot.
If you're making your own chassis, platform, and/or other hardware components you may need tools such as:
For making wiring connections you may use solderless connectors, but you may find that even for that task tinning the wires (i.e., flowing some solder into the strands to make them solid) is necessary, especially if the wire is stranded rather than solid. In that case you'll need
A multi-meter measures voltage (Volts), current (Amps), resistance (Ohms), with more advance models measuring capacitance (Farads), and frequency (Hertz). Places like Jaycar sell multi-meters; I have a BK Tool 2704B, which is good and reliable. But any model that provides volts, amps and ohms is probably fine. Digital is easier to read than the old-school ones with a needle, but needles are pretty cool too. You just have to learn how to read them.
You probably won't need an oscilloscope until you do.
These come in analog or digital flavours. Older oscilloscopes were all analog and a little TV screen in them; most modern oscilloscopes are digital. You can even make a Raspberry Pi into an oscilloscope. See 1, 2 or 3 (there are many web pages if you search for "raspberry pi oscilloscope").
If you really need an oscilloscope for a project and you're local, contact Murray as he may be willing to loan you his Iwatsu (a big old Japanese analog oscilloscope) or bring it to an NZPRG meeting to use.