At last - a topic I can advise sensibly on! There are a number of 'ifs' and 'buts' which may apply, but I'll try to give you a simple guide.
If you want to merely renovate the existing garage to make it into a habitable room (or rooms) you will probably not require planning permission, unless a stipulation was made, at the time the house and garage were built, as to the continued use of the garage for that purpose. This normally only occurs on developments built since the 1980's but it is best to check with your local authority.
If you decide you want to demolish part, or all, of it and re-build to the same footprint, without increasing the overall volume, it will be prudent to check with the planners; they may still say you do not need planning permission but it is impossible to be certain.
The area between the house and garage may be filled in under permitted development, provided that a) the extension to the garage (and any other additions to the original house) do not use it all up. How much you are allowed depends on whether the house is terraced (which I assume it is not) or a semi or fully detatched. If the latter, you are allowed 50 cubic metres or a percentage of the overall volume, whichever is least; unfortunately, I can't recall what that percentage is!
If you are in a conservation area, an area of outstanding natural beauty, or if there are any Article 4 Directives in place, PD does not apply anyway. Once again, check first.
Whatever correspondence you do have with the planning department, make sure you have it in writing, and keep it with the deeds of your house.
Having established what, if any, planning permission you require, and having made the necessary applications (a planning application attracts a fee of ?135 for domestic works) there is the small matter of the building regulations. Now, these will apply whether or not planning permission is needed, as they are entirely seperate entities. I have a feeling I'll have to continue on a seperate post for that.