You can either use butt connectors specifically designed to connect wires of different sizes, which are probably not in stock at your local Autozone, or you can get creative a couple of different ways: either use the same size connector you would use for the stock wire and twist the smaller gauge wire together with the larger gauge on one side, or you can use the inline splice connectors, or, last resort, solder.
I would avoid soldering if at all possible. If you aren't pretty experienced at it, you stand a good chance of creating more problems than you are solving if you get a bad solder joint. Plus, solder generally doesn't withstand the environment of a car too well - it can if done properly, but if you end up wicking excess solder up the wire or use the wrong kind of solder or generally screw it up, it will cause you more issues down the road.
I'm partial to the heatshrink butt connectors available from Waytekwire.com - not only can you get stepped connectors that have different gauges on each side, you can get them with heatshrink tubing instead of that crappy plastic/vinyl you'll find at a parts store. They'll last forever.