A typical 20 foot TV type mast can often be mounted on the ground at the side of your house with only a house bracket for support. Obviously, mounting this same 20 foot mast on top of your roof will get it up higher, but it will need to be guyed, which is more difficult than a ground mounted, house bracketed arrangement.
They do make so called tripod mounts that can be mounted to the roof and a length of mast attached. Depending on the size of the tripod and the length of the mast, it may not require guying, but you need to see if this would get the antenna up any higher than just doing a ground mounted mast at the side of the house.
Also some roof styles are not well suited to mounting an antenna mast on them, like a cement tile roof. An asphalt shingle roof would be easier to attach to, but you would have to make sure any holes you make would be well sealed or you would end up with a leaky roof. Not good! :wink: