Instructions
Buy the power transformer that is appropriate for your particular type of model train. A variety of transformers are available at any hobby shop.
Plug the transformer (which is usually about half the size of a cigar box) into a standard electrical wall outlet. The transformer will convert household current into lower voltage (usually 12 to 16 volts). The train requires this.
Look at the transformer. On the transformer, there will be two screw connections that generally say "To Track." Cut some lengths of low voltage wire to reach from the transformer to the track. Sets of track will often come with a connector clip or screw for connecting a wire to each of the two rails. If not, you can buy such clips separately. If you want to hide the wire connections as serious modelers do, you will need to solder each wire onto the side of each rail. Be careful not to let the wire or solder get onto the top of the rail, or the train wheels will not run smoothly.
Check to see that track sections are connected together with metal clips. These allow the electrical current to continue from one section to the next, so only one set of wires needs to be used between the transformer and the track. If you want to isolate a section of track so it can be turned on or off, then those metal clip connectors must be replaced with plastic ones that do not conduct electricity. You will then need to run an extra pair of wires from the transformer to each of the isolated track sections. One of the wires should pass through a simple electrical switch (single pole single throw -- SPST) to allow you to turn the power on or off.
Try it out. It's finished! The system outlined above will work on any three rail, Lionel type, train track. It will also work on any two rail track, such as HO, N or Z gauge.