There is a $9.99 monthly charge for HD access. You will also need to upgrade your receivers from SD to HD (the HD receivers have a higher monthly charge, but you can probably work out some kind of deal if you talk to the right CS rep). They will also need to come out and upgrade your dish from the round dish to the oval dish (it's about 50% larger than the round dish), since the HD channels are on different frequencies. One thing you'll notice is that the HD channels are much more susceptible to rain fade than SD channels because they are transmitted using narrower signals. So you'll want to make sure that new dish gets installed exactly right or you'll run into a lot of problems. It took several tries to get mine right.
Note: I have not been a Directv customer since 2009, but this is how things were back then.