Correct use of Boolean modifier

At its simplest, I have two objects. The first is a modified block. Then I add a cylinder, shaped like I want. This is to be joined to one end of the block.

If I move the cylinder into the position that I want, it seems I am getting an automatic union of the two objects. If I select the block to begin the Boolean union sequence, I find that both objects are selected. I cannot separate the two objects to try again.

I have to be doing something wrong, but I’m stuck. Any suggestions?

Oh yes, sorry. I’m using Blender 2.81a.

Regards.

Did you add the cylinder whilst in edit mode of the block?

If you select the block and it selects both, when you go into edit mode, if you can select verts/edges/faces of the cylinder, select all of the cylinder and press P to separate it from the block.

Back in object mode, you should be able to perform the boolean operation.