It seems like they aren't really gripping and moving fabric through very well. Is that an adjustment I can make myself or do I need to take it into a shop?

When I place fabric under the foot, it tends to just sit there with the needle going up and down forever. Sometimes I can use the point of my seam ripper to help push the fabric and get it started but not always.

Is it my feed dogs or something else?

I experienced this also when I was trying to sew some flannel. I switched to the walking foot and it seemed to solve the problem. What kind of fabric are you trying to sew?

Muslin and cotton.

Check your stitch length. This happened to me and my stitch length was set at 0.

My machine has an adjustment for raising and lowering the feed dogs. One time I couldn't get my fabric to move and found that somehow the switch had gotten to the lowering position. Check to see if your machine has this.

My machine doesn't have a height adjustment.

I'll mess with the stitch length. Thanks for the idea.

I find my feed dogs don't go up when I use the switch to raise them, feeling beside the feed dogs and pushing upward I found a bar type thing that would raise them.

My feed dogs would not raise into the proper position no matter where the lever was set. After numerous unsuccessful trips and complaints to the dealer where I bought it, I finally took it to another repair shop where it was diagnosed as missing a screw inside the machine that should have been there all along. Once that was finally in the proper position, I could sew and FM quilt. Before the screw, they wouldn't fully go down either which made it impossible to do any free motion quilting. One missing screw made for a very miserable year with a brand new machine.

It sounds like they are not fully up and engaged, or like was already said, your stitch length is too short :D:D:D

Does your machine have a pressure foot adjustment? I had a mechanical machine that would act like that when there was too much pressure. Another thought, did you take your needle plate off and really CLEAN out the lint? It is amazing what can build up in the feed dogs and mess up the way fabric feeds.