If you already have a toilet in the basement on a concrete slab, moving it involves some heavy demolition. Because the piping for the toilet is below the slab, you'll have to dig up the pipe and route it to the new toilet destination. This will involve the use of a jackhammer and the ability to install new masonry over the new drain. The project will take at least two days to complete, if all goes well.
Turn the water off and unscrew the mounting bolts at the base of the toilet with a wrench. Remove the toilet and set it aside. Mark the route for the new drain line to the new toilet installation with chalk or a similar marking tool.
Remove the old toilet flange by chiseling up the concrete around it with a jackhammer and then cutting the flange from the existing piping with a hacksaw.
Dig up the concrete along your new piping route with the jackhammer and dig out about 4 inches of the dirt under the concrete with a shovel to create a pipe channel. Lay the new 3-inch PVC drainpipe into the channel. Once the piping is installed, remove and assemble the piping, using PVC pipe couplings and PVC pipe adhesive.
Chisel out a drain hole in the concrete where the new toilet will be installed. Connect one end of the new pipeline to the old drain line, and connect the other end to the new toilet flange where the new toilet will be installed.
Pour gravel over the top of the new drain line inside of your channel, covering the drain completely. Apply new cement over the gravel with a hand trowel. Smooth the surface with the trowel. Apply cement around the base of the new toilet flange. Allow 24 hours of drying time. Install the new toilet on the new flange by tightening the bolt hardware with a wrench, once the cement is dry.