To drill concrete using a regular drill bit you must start with a much smaller bit and drill a very small hole in the concrete. Move up in bit sizes in 1/8-inch intervals until you complete the hole. You may still lose some drill bits, as they will heat up very quickly and there will be a lot of debris that will need to be cleared. Because of the debris you may have to stop freqently to remove debris from the hole before continuing.
Masonry bits are drill bits especially designed to drill through concrete. Carbide drill bits are masonry bits covered in tungsten carbide, which is a very strong metal that cuts very quickly through concrete and has sloped sides that allow it to remove debris as it drills. Diamond drill bits are regular drill bits covered in diamonds, which allows the bit to grip the concrete as it cuts through.
There are special drills to use on concrete instead of the typical consumer drill. The hammer drill is a large drill used more often by professionals. The hammer is usually heavier duty than a regular drill but it also produces a hammering motion along with the typical drilling motion of a conventional drill. This hammering motion allows it to cut through the concrete much faster. You can usually rent a hammer drill instead of buying a new one since they are only necessary for a larger project.
The older the concrete is the harder it will be to drill through. It may be easier to use a specialized drill bit if you know the concrete is older. Some concrete may contain steel re-bar which would require a drill bit that can also cut through steel. This type of bit is usually only used by the construction industry in jobs that are industrial in nature as opposed to consumer applications.