When changing your starter, the most important connection you can make is from the battery, which provides the power, to the starter itself. There are only two possible connectors, but making the wrong choice can damage the starter, the battery, or both. You'll therefore need to be careful and know exactly where to make the connection.
The short answer is that the red cable connector clamps to the positive terminal, and the black cable clamps to the negative terminal. This will be true whether you're replacing the battery or the starter. Replacing the battery is more common, since batteries typically have a service life of no more than seven or eight years, even for the best brands, and most have less of a lifespan.
When replacing the battery, unscrew the connector clamps to pull the cable connectors loose. Then loosen the clamps holding the battery to its mounting and pull it out. Place the new battery by clamping it to the mounting and replacing the cable connectors, red to the positive terminal, and black to the negative terminal. In many cars, the negative (black) cable connects to the chassis or engine frame, because it's the ground wire.
The process for removing and replacing the starter is very similar, but usually much more difficult because the starter is almost always underneath the battery in the engine mount. For that reason, most people usually defer starter replacement to a trained mechanic. If you do decide to do it yourself, you'll first need to disconnect the battery to avoid getting a shock. Then, determine if the starter solenoid is separate from the starter. If the solenoid is internal to the starter, you only need to remove one set of electrical connections, positive terminal first. The cable connecting the battery to the starter will be the red (positive) connector, and it will be one of two branches of that connector from the battery. The other branch will go to the alternator. Finally, unbolt the starter from the chassis and replace it with a new one by reversing these steps.
If the starter solenoid is separate, however, you'll have an extra set of connections. In that case, the starter cable connects from the starter to the solenoid, and the battery cable connects from the solenoid to the battery. The negative connectors in either case connect to the chassis as ground wires.
