If you're using a stitch regulator, be sure also to check the tracks in which the machine travels forward/back and side/side. The stitch regulates with a wheel (one on each direction) by triangulating with your speed (math way above my pay grade, but that's the way I understand it). If the tracks are not clean, then there are interruptions in the way the machine calculates - ergo, skipped stitches. This problem can give you fits, especially if it continues happening after you've cleaned and oiled the other parts, replaced needle, checked to be sure you're using quality thread, etc.
The best thing(s) I use to clean are kitchen wipes (no bleach) and even bits of batting. Also, if your machine has sat around for awhile, it could be that the innards oil has got gummy. In that case, you'll need a service call to properly clean it out. Check to see when it was last used. If it's more than a few months, that could very probably be the problem. Also, see if any oil that may have come with it has picked up a yellow tinge. If so, it's old. Throw it away and get some SEWING MACHINE OIL that's clear. What yellows the oil is a bacteria which also makes it gum up. The clear stuff is still nice and sterile. Also check your manual for a very small hole in the main sewing machine case. That is the only point you should oil and then, only a drop or two once a month or so.
Hope this helps. There's nothing more fun than a machine that performs properly. If the machine could talk, it would likely say, "There's nothing better than having an informed, conscientious owner." Have fun with your new-to-you baby.