If you're dealing with a small patch of weeds, picking them out by hand is the best and most cost-effective method to get rid of weeds from a gravel driveway.
If the weed snaps in half while pulling, use a screwdriver, trowel, or fork to dig in deep and pull it out from the root, as a new weed may grow from the leftover root.
Alternatively, you can use rock salt. Since it contains sodium, sprinkling the salt, or mixing it with water, will dehydrate weeds, disturb water balance, and kill them.
You can also use a weed burner, which is perfect for long driveways, as it will burn weeds to the root and prevent them from growing back in the near future.