These platforms are as wide as entire football fields and stand at least 10 to 20 stories tall.
Most offshore drilling vessels/platforms are designed to be moved from location to location. The majority of exploratory wells drilled are failures, so it would not make sense to build a permanent structure at the start of a drilling campaign. We use a variety of styles of temporary/mobile structures to drill exploratory wells (and often to drill the development wells, too). These are called Mobile Offshore Drilling Units (MODUs).