Bricks and plates with cheese slopes
The symmetry of LEGO bricks is amazing. The small cheese slopes can, for instance, be used to attach a plate to a brick. This technique is very sturdy, and there's a good chance you will need to get the slopes out with a knife or something similar. I personally use a small pair of pliers.
To find the different pieces needed for this technique you can search LEGO's online Pick-a-Brick for the design ID's. We link other market places directly on each individual piece page, which you can find below.
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It looks weird, but works really well.
The completed construction looks like a plate and brick glued together. Except they're not.
I tried to render an image with transparent bricks to show what it looks like from the inside. Need to tweak those settings a bit, but still looks pretty neat.