Use a stud finder to identify studs in your wall if you're working with wood. You should secure your railing brackets to these for extra support. You'll need a high-quality, sensitive stud finder if you have thick paneling on your walls. If you're dealing with brick or masonry, this won't be necessary.
Measure where your railing brackets will need be screwed into your wall. Building regulations dictate that railings must be installed between 34 and 38 inches above the nosing of treads and landings. If you have young children in your home, consider installing your railing towards the bottom end of this range. If you're not attaching your brackets to wall studs, they should be equally spaced along the length of your wall. Mark where your brackets' screw holes need to be drilled with a pen once you've measured their position with a tape measure.
Attach the appropriate drill bit to your drill for your wall type and the screws you're using. Then, drill holes for your brackets' screws in your wall.
Inset rawl plugs into the holes you've drilled and screw your brackets into place.
Attach your railing to your brackets as per the manufacturer's instructions. The method for doing so will depend on the type of railing and brackets you've chosen.