My cut did nothing

You wired up a Difference, the shape you wanted to cut with is right there, and the result looks exactly like it did before. Nothing broke and nothing changed.

Almost always the cutter is not actually inside the thing it is cutting.

The cutter has to overlap

Difference removes the part of the base that the cutter passes through. If the two shapes do not touch, there is nothing to remove, so you get the base back unchanged.

This is easy to miss because both shapes are usually visible in the viewport and they look close. Close is not enough. Drag the cutter until it clearly sinks into the base, and the hole appears.

A cutter also has to pass all the way through to make an opening. If it stops inside, you get a pocket rather than a hole, which is often what you wanted anyway. Make the cutter noticeably deeper than the thing it is cutting and you never have to think about it.

The opposite problem

If the result vanished completely instead of staying the same, the cutter is now bigger than the base and has removed all of it. Shrink the cutter, or move it back so only part of it overlaps.

Why the shape matters

Difference works on solid, convex shapes: boxes, cylinders, cones, hulls. Feed it something already cut, joined or bent out of shape and it treats that shape as though it were a plain block, so it can take away material you meant to keep.

The rule that saves the most time is to cut first and reshape afterwards.

Avoid a UV sphere as a cutter. Its triangles collapse to slivers at the poles, and that is the one arrangement the cut cannot resolve. An Icosahedron is the round cutter you want.