I've found that I have ripped so many times that I'm getting better at it...
Things that have helped - use smaller needles to pick up the stitches. You can go down several sizes (or use a needle and thread through the stitches and then transfer) since the needle you knit ONTO determines the size of the stitches after you get them reloaded.
I pinch the piece of knitting hard over the next several stitches so when I am tugging on one loop it doesn't unravel the next ones. If I do accidentally run one stitch down, I grab it at the level below and keep on moving, then run it back up when I come to it during the first round I knit after I get everything back on the needles.
AND, I don't worry so much about getting the stitches on in the correct orientation. I just get them on whichever way is easiest, then I correct so all the stitches are facing the correct way on that first round after getting them picked up. Hope this helps. When I first started knitting I had a lot more trouble, but I make lots of mistakes so I am getting better at picking up!