How'd we get here

  I started tinkering with a garden at our new house last year (2012).  I've never really had much success with gardens, though I've been trying for decades.  I was horrified to dig up the yard and find nothing but thick red clay.  Turns out this was a blessing after all, as it forced me to change my methods.  For future reference, if what you've been trying doesn't work, try something new.
  I was listening to an episode of The Survival Podcast (great gardening info in there), and heard Hugelkultur explained for the first time.  Essentially it's adding a buried layer of wood to decompose over time (years to decades depending on the size of the logs).  As the wood decomposes, the soil above moves and shifts subtly providing aeration without human power.  Once the wood has rotted well, it becomes an underground "pond" soaking up any rainfall like a sponge, and forcing your plants to develop deep roots to tap into it, resulting in stronger plants and drought resistant garden.
  Well, in  my neighborhood, I couldn't have mounds of dirt so I modified things a bit.

1. Dig down 18-24" or more (enough to bury your logs). I opted to go with branches and twigs instead for a faster start.

"Raised Bed" Step 1

 2. Add your largest logs/branches

"Raised Bed" Step 2

3. Pile the rest of the branches, twigs, and as much nitrogen rich organic matter as you can spare.

As the wood initially breaks down, it is going to take up Nitrogen from your soil.  It will be returned as the wood breaks down, but adding additional Nitrogen now helps this.

"Raised Bed" Step 3

4. I opted to save the sod and return it on top of the wood pile, grass side down.  I was a little worried about grass growing in my bed, but after a full year, there's been no grass (and very few weeds for that matter).
I thought the grass and especially the roots would break down and improve the soil

"Raised Bed" Step 4

5.  I then improved the clay soil I pulled out with some bagged compost from Lowes and surround the bed with some rocks for a more finished look.  If you have a few dollars to spend, should consider building your beds out of cedar (like the pre-fab fence sections at Lowes).
I didn't have extra dollars, and the rocks were from elsewhere on my property where I no longer wanted them.  Win/Win.

"Raised Bed" Step 5

So, did it work?  Yes and yes.

Spring 2012 Garden

 Swiss Chard in the front
 Jalapeno and Pablano Peppers 2nd
 Tomato and Bell Peppers 3rd
 More Tomatoes and Lettuce 4th
 Trellised Zuchinni and Summer Squash in the back

Summer 2012 Garden

Jalapeno

Red Pablano

Suffice it to say, I'm a big supporter of Raised and Woody-core Bed!