A transportable drilling rig having a self-elevating drill floor includes a base structure comprising multiple base towers that can be transported to a wellsite and positioned around an intended wellbore location. A horizontal base frame is installed between lower regions of the towers to form a stable rig base structure, and a drill floor can then be constructed over the base frame and between the base towers. A suitable rig mast can then be erected on the drill floor. Floor-lifting cables are anchored to upper regions of the base towers and disposable around corresponding sheave assemblies associated with the drill floor. The free ends of the floor-lifting cables can be engaged by the traveling block in the rig mast, whereupon the rig's drawworks can be actuated to elevate the drill floor and mast as required and then locked to the base towers.