First thing is to watch for the directional nap at all times! When you're cutting and sewing, always double check that the fabric is the right way because it's super visible with velvet.

When cutting, make sure to use ample pattern weights so the fabric doesn't shift. Also, if you have to cut on the fold, put the fabric right sides together so it doesn't move as much.

I find it easier to use patters where the seam allowance was either generous (1/2") so I could adjust things as I go or 1/4" so I didn't have to cut anything.

When I used a 3/8" seam allowance, the fabric tended to shift and make it more difficult to sew.

Always test your stitches on scraps before you start sewing so you know you've got the right stitch length, differential and tensions on your serger. I had to lengthen my stitch, change the differential and loosen the tensions a bit for my needles.

On your sewing machine, make sure to lower the tension and have a bit less foot pressure so the fabric doesn't stretch unevenly while you sew.

Use lots of pins or clips to hold your fabric while you sew, to again lower the chance of shifting.