Avoid making the problem worse. If the tool you are using is slipping, stop using it immediately. Further slippage will only continue to wear down the screw head and make it harder to remove. Definitely be sure you are going in the correct direction for removal, which is usually--but not always--counterclockwise ("righty tighty, lefty loosy"). Pressing down hard as you are unscrewing will help prevent slippage.
Use a manual screwdriver rather than a power drill. You will be able to put more pressure on the back of the screwdriver (to increase friction) and to go more slowly. Not all drills are strong enough to exert as much torque as you need to remove a recalcitrant screw. Some chuckless drills will actually lose their grip on the screwdriver bit if you put too much torque on them (especially in the reverse direction).
Get more torque with a socket wrench. If you need a lot of torque because you are hurting your hand or you are not getting results, the best tool is a socket wrench, a common part of many professional screwdriver sets. This allows you to get 6 inches or more of lever arm rather than the half-inch or so a screwdriver handle produces. This greatly increases the amount of torque you can put on the screw for a given amount of hand pressure.
Use a screw extractor. The right tool for the job, assuming the screw head is worn but intact, is called a "screw extractor". This is essentially a screwdriver or screwdriver bit which has strong, rough metal threads right on the tip. These are intended to burrow into the metal of the screw head and get stuck there so you can put some torque on it.
Use a screw extractor like a normal screwdriver to remove the screw. Be sure to go slowly, and press down hard enough to prevent slippage and engage the burrowing threads.
If the screw extractor can't get a grip, you may need to drill a small hole into the screw head. You will need a drill bit that is designed for drilling metal; a wood-drilling bit won't survive. Be careful! If you drill too far, you will destroy the head entirely or make it fragile enough that it will snap off, making it even harder to get the screw out. Given the nature of what you are drilling, pieces of metal may suddenly come flying out of the assembly, so wear eye protection!
Try a different screwdriver. If you don't have a screw extractor and don't want to try to get one just yet, you can try to use a different screwdriver or screwdriver bit. A screwdriver with a bigger head may help. Some screw heads can accept either a slot or a cross-head (e.g. Phillips) screwdriver. You may have some luck trying the other kind. If you have them in your screwdriver set, you might also try a Robertson (square), Allen (hexagonal), or Torx (six-pointed star) bit, depending on the shape of the hole you have. You may have some luck if you experiment with sizes.
Tapping the screwdriver into place with a hammer may be helpful. Tap it with a hammer, but be careful and gentle as excessive force will destroy or remove the head of the screw.
Drill out the entire screw as a last resort, and only if the screw is holding together metal objects. If all else fails, it is possible to drill out the existing screw with a power drill and bit of the same size as the screw's shaft. This will most likely remove the existing thread. Possible solutions at this point:
Replace old screw with a self-tapping (thread-forming) screw of slightly larger size.
Use a nut and bolt instead. If desired, weld the nut to one of the metal objects to create a stationary, threaded mount.
If the screw was large enough, install a HeliCoil insert.
You might be lucky enough to have a screw head (or exposed screw on the rear side of the piece) you can grab with some pliers or a hex wrench.
A stripped cross-head screw can sometimes be extracted by using a hacksaw to saw a slot across the center of the head. After the slot has been created a normal slot-head screwdriver can be used to extract the screw.
Try this simple method:(explained for a star screw)
(1) Hold & rotate the screw driver using the dominant hand & guide the tip using the other.
(2) Without applying any pressure rotate the driver in anti-clockwise direction, feeling the traction for all the 4 possible configurations.
(3) Keep going in rounds until you feel the one with the maximum grip(after 1 full rotation).
(4) Stop & turn in clockwise direction to achieve the configuration with maximum grip.
(5) Now put all your strength to push(concentrate more on this because,if you fail the head gets worn out more)& rotate(anti-clockwise) the screw driver - If the screw can be removed by a screw driver, this is your best chance
If you use a screw extractor, it may get stuck to the worn screw and be very hard to remove. You might not be able to use it again, but at least you've gotten your screw out.
Power tools can be dangerous and should only be used with adult supervision. Follow the manufacturer's instructions, and wear eye protection.
Make sure the object you are removing the screw from is well secured, that you have a tight grip on the tool, and that if you slip, you won't get hurt. You may need to use a lot of force, and you don't want that energy directed toward your body.
Metal burrs caused by stripped screws can cause injury or mechanical malfunctions.
Welding is dangerous and should only be performed by trained professionals.
Things You'll Need
Screw extractor, screw extractor bit, or screw extractor kit. $1-$20 in your local hardware store.
Metal-drilling drill bit
Optional - professional welder