Hi Larry, you can use Edit > Trim for surface cutting operations. The boolean commands are more oriented around working with solid volumes, the different variants of boolean (like difference, union, intersection) determine which volumes are kept and which are discarded after intersecting the objects. But if you are only working with open surfaces and no solid volumes at all those won't be able to work well and instead you'll need to use Edit > Trim. The Trim command cuts a surface with either another surface, solid, or curve and then shows you the cut up pieces and lets you manually pick which of those pieces to discard or keep.

When cutting a surface with another surface, if the other surface has edges right on the one to cut it's usually better to use those edge curves as the cutting object rather than using the surface as a cutting object.

So for your case here, select the red surface, then run Edit > Trim, then the trim command will prompt you to select cutting objects. Now select the 2 top edges of the blue surface, the edges that are right on the red surface. After you have selected those 2 edges, right-click in the viewport or push the "Done" button and you'll be at the last prompt in the Trim command where it says to "Select pieces to remove or push Done to keep all". Go select the piece of the red surface you want to remove and then right click and you'll have made a hole in the red surface.

Now with 2 pieces that have touching edges you can select them both and run Edit > Join to glue them together into a joined piece.

Hope this helps, please let me know if you are still stuck.

- Michael