Your HDTV may have a tuner built in for local over-the-air channels. If not you can use the converter boxes available at Best Buy/Walmart to receive the HD channels over-the-air.
You do not need a converter box if you bought a recent HDTV with a tuner.
Type your address into www.antennaweb.org and it will show you the local TV towers around your home and let you know if you can use an indoor antenna or need an outdoor one.
Often you just hook up an antenna and go into the TV setup menu and have it scan for channels and you can usually get a few HD stations for free.
If you are lucky enough to use an indoor antenna, the Phillips Silver Sensor - Classic version is a good antenna for about $25.
What do you want to convert? The television should already have a built in digital tuner. This will receive Freeview broadcasts, but they're not in HD.
The only way that you can receive HD television programmes at the moment is to invest either in satellite (Sky HD or Freesat HD) or in Cable.
If you wait until the end of next year there will be HD programmes available on Freeview but you will need a special Freeview HD box to receive them, and connect it to the telly with an HDMI cable. These boxes are not on sale yet.