Skulltulas are less dangerous when they are on the ground. They are very easy to dispatch of as it only really takes two hits to kill them, an upward slash to knock them onto their backs and a final Fatal Blow to kill them. If you ever get the chance to do so, cut them off their webs to kill them, it's very easy to accidentally get hit when you attack them and rebound.
They (AFAIK) only come in two forms, hanging on a web string and will go down to your level when you get close or on a full web usually facing you.
When on a string, you could use your Beetle on the string to cut them down. Otherwise if you don't have it (or don't want to pull it out and rather fight them), you need to find a way to turn them so you can attack their weak spot, their bellies. To do that, do one horizontal slash (in either direction) so they are knocked to the side and spin around. After they spin (you may need to wait a bit), they should be turned around so their bellies are facing you. When that happens, do straight stabs forward to attack and kill them. Just be careful of the rebounds when they swing.
When on the webs, you have a couple of options. It should be easier to get past them as they usually don't move.
If they're on a web but are sitting at ground level, try to get behind them if possible so you could forward stab them in their bellies. If not, you'll have to cut them down so you can fight them on the ground. Just cut at their webs and they'll eventually get off to fight.
If they're on a web but not at ground level, you can actually just go though the web with relative ease. Run toward the web and at the last second, roll (shake the nunchuk). You should be able to perform the roll almost completely through. You'll get caught in the web for a second but will break free almost immediately. At this point you could go on or turn around and finish it off using the strategies when they're at ground level.