A pedestal sink saves space in a bathroom but may require adding extra wall framing for support. The project will probably require several days: On the first day, install the framing and patch the wall. On the second day, finish the patching and paint the wall. Install the sink on the third day. (If you have a tiled wall, consider cutting into the wall in the room behind the sink to install the framing.)
A pedestal sink that actually sits on the pedestal makes the plumbing installation difficult and repairs nearly impossible. Buy a sink that mounts on a wall bracket and has a pedestal for looks only. Supply lines that are close together can be hidden behind the pedestal. Otherwise, let the plumbing show.
About 5 hours of work spread over three days
Drywall saw, drill, hammer, taping blade, sanding block, paintbrush, screwdriver, adjustable wrench, groove-joint pliers
Installing a bathroom faucet with pop-up drain, connecting a trap, cutting drywall
Locate studs behind the wall near the plumbing
Pedestal sink, bathroom faucet, supply tubes that fit the stop valves, plumber's putty, 2x6 or 2x8 piece, screws, drywall, joint compound, drywall tape, paint
Drill two holes in the countertop, one for the drain and one for the faucet. There is no overflow, so use an umbrella drain (shown) that covers the drain but does not close it. Apply silicone sealant and anchor by tightening the nut from below.
The faucet unit comes with flexible supply tubes already attached. Apply silicone sealant to the bottom of the faucet and drop the lines through the hole in the countertop. Anchor the faucet from below by tightening the nut and leveling screws.