That old doorbell that you bought at a garage sale may have a unique sound, but if it doesn't have a transformer built in, you need to buy one. Check your doorbell input voltage for either 10 or 16 volts, and make sure that your transformer has the same output voltage. Then place your transformer in a convenient location where you can plug it into a wall socket. Next, you need to figure out how to get the wires through the house as neatly and safely possible, since all houses have different characteristics.
Connect the transformer to the doorbell. Run one wire from either side of the transformer output screw connections (there are only two) to either of the two screw terminals on the doorbell. Strip the wire about 1/2 inch at each end, slip it under the screw connector and tighten the screw with the screwdriver.
Connect the transformer to the doorbell button. Run another wire from the other transformer output screw connection, one of the two screw connections on the doorbell. Strip the wire about 1/2 inch at each end, slip it under the screw connections and tighten the screw with the screwdriver.
Connect the doorbell to the doorbell button. Run a wire from the other screw connector on the doorbell button to the other screw connection on the doorbell. Strip the wire about 1/2 inch at each end, slip it under the screw connections and tighten the screw with the screwdriver.
Connect the standard wall plug to the two wires that came attached to your doorbell transformer. They should be black and white. The exact connection procedure will depend on the type of plug you have. It may have screws to take it apart, or it may snap apart. Inside it probably has two screw connectors to attach the wires to the prongs.
Insert the plug into a wall socket and test the doorbell.
Transformers with 10-volt output usually operate doorbells and buzzers; 16-volt transformers operate chimes. If you have trouble finding easy and neat ways to wire your doorbell, you might consider a wireless, battery-operated doorbell.
You may have difficulty finding ways to hide your wiring. But if you don't put it inside the walls, be sure to put it out of the way of foot traffic to prevent tripping or breakage.