If its a small room, and a cheap carpet with no underlay, then its pretty easy - you just glue it down around the edge starting at the straighest edge. We did a couple of rooms in our first house and they looked fine.
DH fitted the carpet in our back bedroom, mainly because we had a spare bit of carpet and we were a bit skint. It's ok, but it is not completely stretched evenly, and you can tell that it wasn't fitted professionally. Also, it took him ages and was hell on the knees.
FWIW we bought a remnant for dd's room, £80, and then paid £40 for the same company to fit it. It took them about 10 mins iirc with the right tools. It would have taken dh A LOT longer than that. Well worth the money imo. Wouldn't attempt it ourselves.
The knee kicker thing they use to stretch the carpet is £30 for a basic one, by the time you have bought that you could have paid to have it fitted!
Cost us £30 to have a carpet fitted in a 10' X 9' room.
It is one of those things (like plastering) that looks easy and isn't. When they fitted the carpet the bloke was training a young chap and we watched (having a toddler is a great excuse to watch workmen) and it was a lot trickier than I thought!