I reviewed a number of different sites and sets of instructions in order to get a good idea of how I wanted to build our three wicking beds for our garden here in Austin Texas.
You will notice some similarities between my build process of others but I hope to point out a few things that might help you in your build.
Additional pictures of the project and reference material can be found at http://coknown.com/project/1338

Step 1: Materials List

Your materials list will depend on the size, number and shapes of your wicking bed(s). I had a specific area in which to build our 3 beds and consequently designed shapes that would allow for maximum use of the space while still allowing us to easily move a wheel barrow around as well as tend to and harvest from the plants.
Its a good idea to draw out your plan with relatively accurate measurements and even better if you can stake it out at the site to get a solid sense of what its going to look like when its done.
The basics are wood, rock, PVC pipe (or some other water delivery pipe), landscape fabric, heavy duty plastic and soil.
I used cedar to build our beds as I wanted them to last, cedar matches the cedar fence close by, and I didn't want any leeching into the soil from pressure treated products. I've read, by not confirmed, that if the bed is completely lined in plastic then there shouldn't be any leaching of the pressure treated product into the soil. Makes sense I suppose but I still didn't want to go that route even though it is cheaper to use PTP as opposed to cedar.

Step 2: Select a Flat Area

If you have a flat area upon which to place your bed, great for you. If not, get ready for some digging. Make sure the area is as flat as you can get so that your water reservoir will be consistently deep enough to keep your soil wicking.
Luckily for me, the area I picked only had a slight grade and by using a line level it only took a small amount of digging and redistribution of dirt & rock to get the area level.
If you have staked out your beds and know their location, by using a line level you'll have a very good idea of how much dirt you'll have to move to get a flat area.

Step 3: Build & Assemble Beds

Once your area is prepped you'll want to build your beds, line them with heavy duty (4-8mm) plastic, put down the rock, cut & drill the PVC (or other) pipe to fit and test for leaks.
Depending on the size & shape of your beds, you'll have to determine the best way to make them structurally sound. Two of mine are 12 feet x 4 feet and one is 8 feet x 4 feet. All 3 are 15 inches deep. Keep in mind that soil will wick water up approximately 1 foot. Consequently, you want to account for how much soil you need for the kinds of plants you want to grow vs how much the soil will wick water.
A word about the rock. For the first layer, I used round pebbles (landscape rock) from a local big box store. The second layer of rock I used was volcanic rock to fill up the 3.5 inches I wanted for my water reservoir (covers the 3 inch PVC pipe). You don't want to put volcanic rock on your heavy duty plastic as it might puncture your plastic and destroy your reservoir.
As for drilling the PVC, whatever large bore bit you have, use that and stagger holes along the side and bottom of the pipe every 6 inches or so. You'll also want to cap the end of the pipe so all the water you pour in doesn't rush out the end as opposed to being evenly distributed. I didn't use a PVC cap but instead stuffed old (but clean) rags into the ends of the PVC pipe so the cloth would allow the water to leak slowly.

Step 4: Soil, Trim & Ready to Plant

Calculate how much soil you'll need using one of the many online calculators. I highly recommend you buy good quality soil. There are lots of recommendations out there for soil preparation so I won't go into that. Read up on it and make sure you put in the best you can find. You don't want to try to save money on this step.
Once you've filled your beds with soil, trim away the excess plastic and you're ready to plant.
Again, I have many more pictures and other reference pages available http://coknown.com/project/1338
I'd also be happy to answer any specific questions about this project.

Thanks for reading through this.
Next up will be my water harvesting system.