Go down to Sealine in Messaid, and you will find alot of divers around there. You can hook up with anyone there and enjoy a dive. 15meter depth, vis is about 5m-10m, depending on tide and wind. Some old cars, bus and artificial reef. 

Pearl divers in Al Nasir street, Al-Sadd is where you can rent tanks, or full gear if required.

There are some other spots around, but this is the easiest for a quick splash. 

There are quite a few jellyfish in the water around here, so suggest you dive at least with a full lenght skin suit.