I have a basic understanding of depth. Back when I did a guide to making things look good, I mentioned adding curves to houses, forming alcoves and whatnot. There was also the little awning I added over the front entrance. Those are pretty basic. There are a few areas I will look into right now.
Canvas Technique
My experience indicates the key aspect of adding depth is what I call the "canvas technique." In it, you take a wall and around its perimeter, adding support beams on the top and sides.
Let's compare the one on the right with my standard build style.
The one on the left, my typical style, doesn't look half bad. But on the right I have moved the blocks out an additional unit. Granted, this required squeezing the smooth sandstone blocks in (so there's only a tiny space inside the right one) but it is rewarded from the new level of depth shown here.
I call this the canvas technique because with the log support pillars, it creates a sort of "canvas" we can then decorate. There are tons of way to do this. Foliage seems to be a popular and logical choice.
You might also use fences, fence gates, and the cobble/mossy cobble walls. After some quick experimentation, I find fence gates to be rather nice looking.
This kinda fits here. A nice technique I came across was using stairs above and below windows. I imagine this doesn't work as well if the stairs don't match the blocks making up the wall.
You can expand the support buttresses as far as you think is appropriate. Nice touches can also include stairs, fences lining them, half-slab awnings, and so on. This picture right here is probably the most depth-laden piece of work I've ever made. If you add a wooden button on each of the smooth sandstone blocks that aren't covered by a fence gate, it adds a little extra.
Roof Design
A long time ago I wanted to put together a tutorial on making roofs. It would have been as useful as me as for anyone else. Roofs are surprisingly good for adding depth. The most basic measure of adding depth is extending roofs outward. Here is what I mean. Consider the roof module on the left, and the one on the right. The right one adds depth and in my eyes, is very nice.
One on the right is a bit more festive, wouldn't you say? You can also add the extra stuff like fences and whatnot to a roof unit as well, for added depth and detail.
Put It All Together
I went ahead and tried making a house using the depth techniques I've mentioned here. It could probably benefit from having a door, but this is stuff I'm still new to.
Others' Work
A really good way to get better with depth is to mimic the works of others. There are many Minecrafters out there who seem to have a natural talent at depth. Try watching their stuff and recreating their builds yourself. Add a little variation if you can come up with one. This will give you hands-on experience in depth and detail. This in turn will give you a feel for it and you'll be able to reproduce the skill.