Having outdated wiring in your house is not a matter for immediate concern if everything is working. When you want to add computers, new lighting or a circuit for an extra room, however, old wiring may be a problem. Modern electricity codes require grounding for all residential circuit elements, so the first thing to do is make sure your panel is grounded. Then you should be able to remove and replace old wiring by fishing it through the attic. It won't be easy, but it's better than tearing the walls off.
Ground the house panel by connecting it with 10-gauge grounding wire to a ground rod pounded into the earth. If the panel has no ground buss, replace it with a new one. This will be easier and safer than grounding individual circuits or circuit elements.
Disconnect circuits that you are going to replace by removing the leads from the terminals. This will prevent anyone inadvertently switching on the power while you are working.
Disconnect the first element on the circuit, such as a switch or receptacle, and remove it from the electrical box so you have room to work. Join the end of the new wire to the end of the old one with electrical tape, wrapping the tape so that both ends are covered and the transition is smooth.
Find the place in the attic, at the top of a closet or under the floor where the wire enters the wall and pull it out, installing the new wire into place as it goes. If the wire is stapled to a stud, cut out a section of drywall so you can remove the staples. This drywall is easily replaced. Wherever you have access, staple the new wire in place.
Work backward in this way until you get to the service panel. Leave enough slack so you can connect the wire later.
Find the circuit element that is next in line on the circuit. If the original element was a switch, the next one is probably a light. If it is a receptacle, the next one may be another receptacle. Disconnect and remove that element. Attach the new wire to the wire at the original element and pull the old wire out of the electrical box of the second one. Continue along the circuit in this way until you have fed new wire to all circuit elements.
When all circuit elements have been rewired, connect the wire to the panel. Remove a length of sheathing with a utility knife and separate the wires. Strip 1/2-inch from the ends of the insulated wires with a splicing tool and connect the white wire to the neutral buss, the bare wire to the ground buss and the black wire to a circuit breaker. Then snap the breaker into place on the hot buss.
Leave old wires in place if you can't pull them or remove the staples. Cut off as much as you can and feed new wires to the boxes from the panel. Use fish tape, which is a kind of spring-loaded wire, to pull new wire through conduit and other difficult-to-reach places.
If you need to make a new pathway for wires, work from a closet or remove a small section of drywall and drill holes in the top or bottom plate of the wall, running the wires as much as possible through the attic, basement or crawl space. Update circuit elements with the wiring, replacing old ones with ground-able new ones.
Always disconnect the power before you work on electrical wiring.