Sky King has good advice, as always. There's a lot of text there, so if we double-up, well, then you know it's good advice. (I haven't had dinner yet, didn't eat lunch and breakfast was a long time ago, so...)

1. Core strength. The hardest to insta-fix, obviously, but it helps loads.
2. Make sure that your saddle isn't tilted too far down. I wouldn't move it if it's in the right place for your knees, but check the tilt. I think the rule is no more than 2-3 degrees of tilt. Try leveling it or tipping the nose up a hair and see what that does for slipping forward (if that causes pain in other areas, see step 4). Also consider dropping your saddle a smidge.
3. The bike, as set up, is too long. With too long a reach, you end up sliding forward on the saddle and your weight rests on your hands and wrists rather than on your butt. (Been there, done that, got the T-shirt.) Go back to the shop. You may be able to get away with moving spacers around, although most shops set the bikes up in the least-aggressive position possible, or you might need a shorter stem. It's a pretty simple part to change out, and not very expensive. Don't move the saddle unless the current position makes your knees hurt.
4. The saddle itself. It might be that it's too narrow, so you put more weight on your wrists rather than soft tissue, or just the wrong shape so that the pedaling motion causes you to slide forward. (Very wide or "pear-shaped" saddles with a very gradual transition between the nose and the "seating area" can cause this problem--got that T-shirt too.)