How can I tell if a slab foundation can be built on?
The first step is to look at the foundation that supports that the walls of the garage. If the walls have foundations separate from the garage floor slab and those foundations are similar in construction and depth to those of the main house then this is a good indicator that you are in a good position to proceed with the remodel plans. 

On the other hand if the slab was poured with integral footings around its periphery that are similar in size and depth to those of the house then you are also probably good to go forward.

If the garage is simply a thin floating slab then a whole lot will depend upon the climate in your area, the type of soil, the lay of the land and local code requirements. You may be in a good position if the "attached" structure of the garage to the house is sound, the slab shows no signs of cracking and shifting and the construction technique is up to code. 

In any case it may be well to check with the local permitting authorities and/or bring in a consulting local contractor to give you ideas and make suggestions.

One last thing that comes to my mind regarding this potential project is the evaluation of whether the garage slab is below the floor level of the original house or not. If it is below you may very well want to consider the possibility to build up the floor to the level of the house. This will help to make the added living space feel like proper part of the house and make movement into and out of the space a whole lot more natural.