The yarn you've just made is a single strand, called singles. You can use singles for knitting or crochet, although knitting with singles isn't really recommended (the stitches tend to pull on a bias in unpredictable directions). To best use your handspun yarn, you'll want to ply it.
Before using or plying your yarn, you'll want to wind it into a ball. Untie the store-bought yarn from around your skein first of all. If you have a ballwinder or a nostepinne you can use them, but otherwise you can just start winding the yarn around a finger, slip it off your finger, and continue to wind. But one big warning here: you'll want to have the skein hooked around your (clean, bare) feet or have someone else hold it around their hands; otherwise the skein will get tangled and it'll take you a million years to untangle it.
Once your yarn is in ball form, you can use it. Or you can spin another spindleful of yarn, set the twist, let it dry, and wind it into a ball too, and then you can ply the two balls together.
Plying
Plying goes a lot faster than spinning, don't worry. Put the balls of yarn into two coffee mugs or small mixing bowls so they won't roll all over the room while you're plying. Hold the two ends together and tie them to the end of your leader. Hold the spindle and yarns just like you do when you're about to spin roving, although you should keep the two strands of yarn separated between two fingers (so they won't tangle together before they're plied).
Twist the spindle sharply--to the left! Yes, you ply backwards from the direction you spin, and that's why you always want to make sure you spin your yarn with twist to the right. Allow the two strands of yarn to twist together, but be sure to get plenty of twist into them. The yarn may look well plied, but it's amazing how much twist it really needs.
Once you've plied all your yarn together, it's done. You don't need to soak it again. Wind it off the spindle into a ball and it's ready for anything. Make sure you admire it a while, too. Doesn't it look beautiful? It looks like real yarn you bought from a store, doesn't it? Plying takes out some of the twist in both singles, and smoothes out some of the slubs and uneven sections.