I am surprised no one has given a link to Dave's discussion of connecting a signal generator to a scope yet. Here it is:
It was linked in the second post of the very similar thread I linked to.
Where do I get that gray high frequency x10 probe that can be connected to the function generator?
It has been a while since I watched that video, but I am pretty sure it is just a basic x10 scope probe (could as well use a switchable 1x/10x probe set to 10x). Many probes come with an adapter that lets the tips connect to a BNC socket. I do not think these adapters are particularly generic, so I would not assume an adapter from a random other probe to necessarily fit your probes. If your probe did not come with a BNC adapter, it might come with one of the springs that fit around the ground sleeve and provides a very short (low inductance) ground path. This is easy to fabricate from a piece of wire (wind it around something with a slightly smaller diameter than the grounding sleeve). But that would mean having to hold the probe.
Am I right that if I also feed in the signals from the function generator to the electronic circuit, I get a BNC T adapter first. Connect one end of the T adapter from the function generator to the scope via the the high frequency x10 probe. The the other end of the T adapter to the circuit via some kind of grabbers/clips, or other connectors like pin headers? Not sure what DUT mentioned by alm means.
DUT = device under test, i.e. whatever device you are measuring. Might be a circuit on a breadboard, or a piece of equipment you are repairing, or a single component, whatever.
For the typical application of using the generator to provide a signal to the DUT, for example testing the gain of an amplifier, you would typically connect the generator directly with a cable to the DUT (this is where something like grabbers or hooks might come in handy), and use a scope probe to probe whatever point of the circuit (could be for example the input and output of an amplifier). Whether you would need to terminate your generator at the DUT depends on the input impedance of your DUT and the frequencies involved (for audio you typically would not bother).
You would not usually connect the scope directly to the generator unless you were testing either, or as some sort of baseline. But in my opinion things like BNC-BNC cables, tees and terminators are basic lab equipment, so it is not bad to have them.