A velvet dress is the one you reach for when the usual black dress feels too flat and jeans feel too little. It does the job of smart without trying hard, the kind of thing you can wear to a dinner, a carol concert, a work party, and not feel like you've dressed as someone else for the evening. The fabric does most of the talking, so the cut can stay simple.
Fit matters more here than in almost any other dress, because velvet has no give to speak of and shows every inch it's short or long. I'm tall enough that most midi lengths land somewhere between my knee and my shin, which is its own particular kind of wrong, so I check the hem against my calf before I check anything else. A velvet dress that's meant to sit mid calf and instead stops at the knee reads as a different dress entirely, not a shorter version of the same one. Watch the sleeves too, since velvet sleeves that are even slightly tight pull across the upper arm in a way that a cotton sleeve never would, and a waist seam that sits an inch high will sit there all night, it doesn't settle. If you can, sit down in the changing room. Velvet across the thighs when seated is where a cheap one gives itself away first.
The difference between a good one and a sad one is mostly in the pile and the lining. Cheap velvet goes flat and shiny at the elbows and across the seat within a few wears, and once it's crushed like that it doesn't recover, no amount of steaming brings the nap back up. A better one has some weight to it, holds its colour in both directions when you brush it with your hand, and is properly lined so it doesn't cling or ride up when you walk. Check the zip too, it should sit flat and not pucker the fabric either side, because a puckered zip on velvet is visible from across a room.
For pairing, I keep it plain. A plain coat rather than a patterned one, a boot rather than a strappy sandal unless the occasion really calls for it, and jewellery kept to one piece because velvet already has texture doing its own thing. If you've none in the wardrobe yet, start with a dark neutral, bottle green or a true black, in a long sleeve midi, since that's the version that covers the most occasions without feeling costumey. Steam it rather than iron it, and always from the lining side if you can.