More often for reduction in price of garage to not make a basement, that a principle it is justified, but for that to make garage warmer and damp-proof it is possible to make a small basement. For this purpose it is necessary to lift a small basement above the foundation about 20-30 sm, the grounds necessarily are higher. Do not overlook, that the basement is carried out only from a red brick, silicate to use it is impossible (though the some people use, but it is not recommended). Also it is possible to use rubble a stone or cyclopean concrete.
The width of a basement should be same, as well as at the foundation. After the basement is ready, from above it is necessary to lay roofing material (ruberoid) in two layers, necessary with overlapping, it the moisture will provide tightness. On edges, make so that roofing material stand out on some centimeters.

If the basement is ready then can proceed to walling of garage.