Always lay out velvet with the pile down on the table and the reverse of the fabric looking at you. This way you will be able to mark out your pattern pieces clearly. I prefer to use pattern weights and mark around the pattern pieces. Then make sure you cut on the inside of the line so you’re not adding any extra into your pattern piece and very slightly altering its size.
If the pattern piece is normally cut on the fold mark around one side of the pattern piece, then flip the piece over and mark around the mirrored side. To save time you can always recut the paper pattern piece as a whole and then mark and cut around the whole piece in one go. I much prefer to do this as it saves time overall.
If you would normally cut a pair of pattern pieces on doubled over fabric remember to flip the pattern when you cut the second one so you have a pair and not just two the same.
Use a rotary cutter if you have one. I have used a sharp scalpel in the past as this way you will not cut into the pile too much. But a sharp pair of shears will do a good job too. I also have a vacuum cleaner close by when cutting velvet as the piles just goes everywhere!