The caves were originally pretty much just renovated to have supports so there wasn't a lot to maintain. Later, this was renovated to be used as part of the underground railroad which put in a lot of secret passages and minimum structural stuff there. This was then built up a bit more for usable space.
After several devestating events the caves (Read No Man's Land and the surrounding books) were built up and are more like a high tech basement than a cave. Much of the work was done by regular crew men creating structure and support for the new re-creation of Wayne Manor.
Any work and maintenance that needed to be done from a while before the the Knight Saga up until the Hush Saga it was done with the aide of multiple private sworn to secrecy type contractors, Harold Allnut, Bruce, and any extra help from the rest of the bat-family.
By the time of the Hush Saga the cave is much more automated and much more like a regular basement room than "caves" and as such doesn't really need maintenance or work done on it, but anything like that is done by Bruce and Alfred using various means to keep it a secret. (For example, he has a suit that gives super strength. Moving his super computer in and out of the base would not be that hard)
Major work has also been done by other heroes in the DC community, Superman for example has helped out building the cave or cleaning it up.
Any major repairs or overhauls to the superstructure has Bruce and co. removing all the bat equipment or squirreling it away and then bringing in repair crews, but this is rare and as far as I can remember has only happened a few times in the 20-30 years of Modern/Bronze Age canon.