Shut off valve turned on - no water flow
First of all, make sure the valves below the sink are really turned on all the way. Sometimes they get stuck.

Second of all, check to see if the tip of your faucet (the part where the water normally shoots out) has a fitting that you can unscrew. Many faucets have a little mesh piece here that can get clogged. It's possible that's your problem (although if you are not seeing even any dripping, I doubt this is the issue, because it's hard to imagine the mesh piece becoming so blocked suddenly that no water comes through at all).

If you're confident that the valves are on and the faucet head is clear, then it's likely you have a blockage somewhere between the valves and the faucet. If neither hot nor cold water comes, then the blockage is probably in the faucet hardware itself, rather than in the hoses that connect the valves to the faucet. (If the hot or cold hose were blocked, then the other water should still work.)

I'd turn the valves back off, then disconnect your faucet hoses. At that point, turn each of the valves on quickly just to make sure that water comes out of both of them (if it doesn't, then there is an issue with the valves, not the faucet). Next, remove the faucet from your sink (you might have to loosen a nut or two underneath the sink to do this) and see if you can see what is blocking water from passing through it.

Depending on what kind of faucet it is, you might be able to disassemble it into smaller pieces, which would probably help to find the problem. Or it might be a single piece.

If you can't see any blockage, you could try flushing water backwards (i.e., pump water in from the part of the faucet where water normally comes out) through the faucet using e.g., a garden hose, in the hope that that dislodges whatever is the problem.

If all else fails, replace the faucet.