There are two common types of wire connectors in the US (I think other places don't use wire nuts as much):
The classic brand is Ideal, sample here from Amazon. (Amazon gives you a great idea of the range available, but make sure, wherever you buy them, that they are the real Ideal brand or another UL or ETL listed brand. There are plenty of cheap knockoffs which can be dangerous.)
With a wire nut, you pick a size that is the right size for the number and size of wires that you are using. The Ideal Catalog has a pretty complete list, plus each package should show the capacity and Ideal also publishes very detailed specification pages for each type of wire nut.
You twist the wires together a little, stick them in the wire nut and twist really, really tightly. Make sure no wire is loose. That's it. Done.
One catch: copper vs. aluminum. Wire nuts are generally recommended just for copper wires. If you have a mix of aluminum and copper wires, there are special purple wire nuts available which are designed to connect aluminum and copper. But there are complications and that is not necessarily a good idea for the average user.
The big brand is Wago as you have already discovered. You put one (and only one) wire in each hole/lever/connection. If you have a 3-conductor lever nut and only 2 wires, leave one empty. If you have a 2-conductor lever nut and 3 wires, get a larger lever nut or an appropriately sized wire nut.
Lever nuts are a little simpler to learn how to use. They are (at least comparing UL/ETL listed lever nuts against UL/ETL listed wire nuts) more expensive than wire nuts, which makes sense since they are a more complex mechanism. But for small projects this is no big deal. They are also much easier to see if a wire is in properly or not - with a wire nut the best you can do is a pull test and hope for the best.
Lever nuts do take a little more space (not a lot), so if you are really tight on box fill, wire nuts may be a better choice.