Many people think that you cannot drill concrete with a regular drill. They believe that you need a special hammer drill with hardened drill bits. While these tools do make the job faster they are not necessary. You will need a bit more patience and a wider array of drill bits when using a regular drill, but the procedure is the same for drilling in concrete regardless if you use a regular drill or a hammer drill.
Mark the center of the hole on the concrete, and insert a small sized masonry drill bit in your drills chuck. Begin drilling into the concrete applying steady pressure on the drill. If any time you feel the drill bogging down back off some.
Gradually increase the size of the masonry drill bit until you hit the diameter you're looking for. Increase the size of the drill bit by no more than 1/8 of an inch at a time and re-drill the hole.
If you hit a spot in the concrete where you can not get the drill bit to go any further stop and back out and increase the diameter of your drill bit as in step two. Once the hole is slightly larger take a hardened nail, place it in the hole and give a few whacks with a hammer to break up the aggregate you likely hit. Then continue like normal.