From what I've been reading, if you are interested in purchasing one of these "$1" homes, first you need to see if your community purchases such homes from HUD. If they do, then you need to find out if you qualify for the local program to purchase such homes. The homes are not sold directly to the individual families, but to communities that fix up the house and sell it to those who qualify.
One example given was in Gary, IN - qualifications to purchase these homes in their city is your annual income needs to be at least $35,250/year, demonstrate financial ability to bring the property up to code withing 6 months of purchase, and agree to live in the home for a at least 5 years to receive full ownership of the property.
When I was house shopping a few years back, I was looking at foreclosed and short sale homes as potential options. One thing I learned is if you end up buying a foreclosed home, there is a larger probability that the house will require a lot of maintenance due to lack of upkeep by the previous owners. The house may be considered cheap at time of sale, but your expenses skyrocket when you discover everything that needs to be fixed. I classify these under the buyer beware - sometimes you can get lucky, but you really need to do your homework before committing to one of these.
Whether you purchase one of these type of homes, or save up to buy a non-foreclosed home - the most important thing it to ensure your finances are in order so you know you can cover all expenses of the home - not just the purchase price. There's the escrow (property tax on the property, mortgage interest if less than 20% down, property insurance), utility costs (electric, gas, water, sewer, garbage, other...), property maintenance (lawn maintenance, snow removal), appliance maintenance (furnace, air conditioner, washer/dryer, hot water heater, kitchen appliances,...)
Plus all the extras one needs to maintain a house that you don't think about if you rent - tools, ladders, lawn mowers/shovels, filters, etc...
The more prepared you are with the cost of why you'll need to get (either buy new or get on Ebay/Craigslist/garage sales), and the monthly costs of the home - you should do okay.