Once you secure the new strings to your acoustic guitar, you need to get the new strings tuned up. As the string draws tight, hear the string come up to pitch. The easiest way to tune the new strings is to change the strings one at a time. You'll want to tune the new string to the old ones, which, presumably, are relatively in tune.
Both steel and nylon strings need to be stretched out in order to keep the correct pitch. So, once you get the string to the correct pitch, pull on it in various places up and down its length to stretch it out a bit. Stretching the string can cause the string to go flat — sometimes drastically — so tune it again by winding the peg. Repeat the tune-stretch process two or three times to help the new strings hold their pitch.
After the string is up to pitch and stretched out, you need to remove the excess string that sticks out from the post. For steel strings, you can either snip off the excess with wire cutters or bend the string back and forth over the same crease until it breaks off. Nylon strings can simply be cut.
Whatever you do, don’t leave the straight string length protruding. It could poke you or someone standing next to you (such as the bass player) in the eye or give you a sharp jab in your fingertip.
Although nylon strings aren’t as dangerous as steel strings if any excess protrudes, the extra string hanging out is unsightly, and besides, classical guitarists are a little fussier about how their instruments look than acoustic guitarists are.