How do I wire receptacles for a washer and dryer on a new circuit?
Wire from the panel to the closest outlet.  Use Ratchet Freak's recommendation of using a GFCI since this has a potential to become a wet location.  Put the GFCI at the first outlet location and wire the line/feed side of the outlet to the wire running from the panel.  Add a second wire that will chain the second outlet to this outlet.  On the GFCI, the second wire will attach to the load side of the outlet and the other end will wire to a normal outlet.  

For a 20 amp circuit, you will be using at minimum 12 gauge wire.  Make sure the wires are anchored to the studs outside the box and they are running through the middle of the studs to protect from screws/nails.  If you have to notch a stud to run the wires, make sure you add a nail plate over the notch.