Generally the smaller diameter wire that goes along with the heavy wire on the battery cables is cut and crimped into the old wire when installing a new set of wires. You could also solder the joint for best connection.
In doing ANY battery work, always disconnect the negative side first! This breaks the ground with the vehicle and makes for a safe project.
The same goes for using jumper cables as well -- do the negative last on hook up and take it off first when pulling them off. Accidentally hitting the body panel or something under the hood will not light you up if you do it while disconnecting the negative terminal as the body and frame are all hooked to it (the vehicle grounds through the metal, which means that the current return flows to the battery through the vehicle metal structure).
Use good quality cables also. Don't just go by the thickness of the external part of the wire -- some manufacturers like to use really thick insulation, tricking you into thinking you are getting a lot of wire for your money. Use the largest size wire with the finest strands you can find. It will carry the load with the least resistance.