Merging a shape onto another shape and removing excess polygons? Diagram: Black shape is base shape that I want the Blue shape to merge onto. I am guessing I can fix the way they bond afterwards.

I want to merge the two shapes into one so that they are no longer separate in Edit Mode. I then want to delete any hidden faces and maybe tidy up where the ramp faces meet the hexagon as well as delete the submerged base of the hexagon in line with the cylinder top. 

Here is another diagram of what I mean...


Thanks again!
You can bool the shapes directly in Edit Mode, as long as they exist in one single mesh already. If you have two different meshes, joint them by selecting both and hitting Ctrl + J. Then make sure the normals are all pointing outwards (Ctrl + N recalculates normals if they are off), otherwise the boolean operation fails.

Now, select one of the meshes: Select one face, and using Ctrl + L select all connected faces), and using the Spacebar menu search for Boolean, like this: