Technically you want an electrician to do it, but for me it's just a matter of running more Romex across the unfinished basement ceiling, dropping it in behind the drywall, near the outlet I want to create the new circuit with. Then I disconnect the wires heading into that outlet from which the old circuit will remain. Once I instill the new wire into that box and deal with the main electrical panel, all the outlets still connected to that outlet have now become part of the new circuit.
So, there are 5 outlets on the same circuit right now. I'm going to run a new line to the middle outlet. Once I disconnect the middle outlet from those on the right, the two remaining outlets on the right stay on their own circuit. Now, when I connect the new wire, that was fished down behind the wall, to the middle outlet, that outlet and the two to the left of it will be a part of the new circuit.
Depending on access, it shouldn't be hard for a licensed electrician to handle.