I'm no expert, so if my advice is too appalling then maybe it will at least spur someone more knowledgable to post better advice! But here's what I always did and it worked well enough.
I took a small crochet hook - it had been my mom's from her doily-making days - and I slipped it into the knitting near to the snag. I worked the hook up next to the snag, grabbed the 'snagged bit', and then pulled it through to the back side of the knitted material. I then worked my hook carefully back through and removed it, being sure that I left the 'snagged bit' inside between the knitted material and the lining.
I had to be careful of two things:
*That I didn't pull the 'snagged bit' too far along once I was through to the back side -- thus messing up the knit even more.
*That I didn't create a new snag by bringing the hook out of the material too carelessly.
I hid a lot of snags this way, though I'm essentially useless in the mending department. If it's a very long snag, I'd tie a knot in the yarn before pulling it through. Once I also took a needle and thread and tightened up the snagged area a bit after pulling the snag through, just to close the gap.
Hope this helps? :-)