Most ODH veterans wear either well-made running shoes, trail running shoes, or lightweight hiking boots that fit properly and have been broken in. There are many good brands to look at for a good quality shoe; just to name a few:
Given that the trail surface is mostly hard-packed dirt, make sure that you provide your feet with good cushioning and support. Use the training hikes as your guide to what's best for you in terms not only of shoes or boots but also socks and shoe/boot inserts and other equipment.
When purchasing a shoe, make sure that you are fitted properly at the store! If not, you run the risk of the shoe being too small, which could lead to many complications down the road - especially on hike day; and if the shoe is too large, it is much easier to get blisters or worse.
Experiment with taking along a change of socks, or powdering your feet with baby or foot powder to reduce friction (some hikers use Vaseline instead). Keep your toenails trimmed.
Remember - a very common problem that long distance hikers encounter is swelling of the hands and feet. This means that shoes need to be well broken in before hike day. Training hikes are a great way to test them out and get them broken in!
Besides having the right footwear for the hike, having the proper socks is equally important! Cotton is the WORST possible material, since it soaks up sweat and keeps your fee cold, wet, and can easily help to make your feet hurt so badly that you'll have to drop out of the hike!
We strongly recommend a similar sock which is made of a wool and synthetic blend. Wool is a naturally good wicking material, and therefore will keep your feet dry as you hike. Another benefit of this type of sock is that the inside of the sock is actually a knit liner which is built into the sock which helps to again keep your feet comfortable and dry, but also aids in the prevention of blisters.
Please note that socks only go so far though when it comes to blister prevention. A lot of it also has to do with the type of footwear you're using, and how DRY your feet are. Learn more about blister prevention and care on the Trail First Aid section.