If you're talking 'a sphere on top of a cube, then thats not too dificult.
In point edit mode, wireframe view, just zoom in and select/delete the unnecessary 'points' (being carefull that you don't lose any edges that will be visible).
Use the same method for things more complex, but if there's too much going on, obviously it can all get a bit of a confusing mess.
I'm not aware of any magic button, but there is 1 thing that might be worth keeping in mind. That is, that it's not always necessary to join the 2 meshes together. In fact, often it is best not to. For example, if the 2 meshes aren't joined into 1, then you can move 1 away from the other, which may make it easier to select/move/delete unwanted stuff. Then just move it back to position.
When you think about it, the object will stay together when put into scene or figure mode anyway. Joining solids within 1 object is often unnecessary, and can actually restrict what you can do with it in object mode.
I hope that makes sense.