Mostly depends from the screws.
Be calm, and search for other similar questions. It happens more than you think. I too passed under that crucible, but on a laptop.
I take you're speaking of the external screws.
Torx and pentalobe screws are kind of easy to strip, so prevention is in order: your screwdriver is obviously worn out. I stripped badly a Philips 00 with an old jewelry screwdriver, so I bought a new one from a reputable source. If you're not constrained by mailing fees, iFixit has good ones, and even kits with the dreaded pentalobe screwdrivers or their Philips replacements.
Granted you're sure to avoid spills on sensitive parts of the iPhone, there are lubricants that loosens screw enough to help in the operations. Otherwise, it's better act without.
But return to the issue you've got at hand. In order of destructivity to the screw and item you'd need to achieve that (I'll give you later the most effective) you may:
- If there's still at least a couple of recognizable grooves on the head, poke and pry them with a jewelry screwdriver, angling it and trying to twist the screw out.
- You can also try using a slightly bigger Screwdriver, with a bigger handle and a longer shaft, for more torque
- If you've got something to increase the grip, and the screwhead is at least half recognizable, use it. The skin of an old baloon, or some special concoctions you can find on Amazon, acting as a temporary glue. The screwdriver will be able to grip enough to let you loosen the screw, and then you may finish the job with tweezers, pliers or fingers.
- Failing all of that, you're entering in the "danger zone", that is, the point where the screw has to be physically damaged and/or you're going to face expenses to let the little bastard go out. First of the danger zone is the '''acquisition of screw extractors'''. They've special heads that burrow in the half-grooves you've left, allowing you to twist them out. Then, when the Head starts to peek out, you could grip them with your fingers, tweezers or the ESD Screw Extracting Pliers, the smallest measure.
- Failing that, you could coat an old screwdriver with a tiny amount of Gorilla Grue or strong glue (avoid spilling!!) and let it cure on the screw. Then remove it.
- Failing that, or if you're unwilling to get those items, you could use a Dremel with the smallest rotary cutting head you've got, and cut a slot in the screw. Then you may be able to use a flat screwdriver. However we're speaking of massive cosmetic damage, as the smallest dremel head is likely to scratch your iPhone bezel
- Failing all of the above, but only failing all of the above, use a drill of roughly the same diameter of the screw shaft, and drill the head out, removing the shaft later with pliers. If you can find a drill small enough.
The safest course of actions passes through the use of the Screw Extractors, after evaluating that the screw is unable to be removed with other screwdrivers.
The drill is the last resort, use it only after everything else fails. The glue method and the dremel one seems commonplace, but the Extractors can always be kept for later occurrencies.
You will still need replacement screws however: some Apple Geniuses could be helpful enough to provide you with help and spare screws (they buy them in stocks) for a nominal fee.
Four different sized extractor tools to help remove fasteners or screws with stripped heads. Driver head is claw shaped for maximum grip. Sizes range from 1.1mm to 2.0mm. — 50+ available at 19.95 each.
Pliers designed to firmly grip the heads of damaged screws. Specially designed jaws firmly grip screw heads, bolts, or nuts allowing you to twist out even the most damaged fasteners. Professional Grade tool. ESD-safe option. — 50+ available at 29.95 each.
All the parts and tools needed to replace the 5-point pentaobe screws on the bottom of your iPhone 4 or 4S with Phillips screws. This way, you won't need special tools if you have an iPhone repair emergency. Compatible with all iPhone 4 and 4S models. Inc — 50+ available at 9.95 each.
All the parts and tools to replace those pesky Phillips screw with the oppressive 5-Point Pentalobular screws. — 33 available at 9.95 each.
The easiest way to fix this problem is to simply file the tip of your pentelope screwdriver down until the grooves are big enough to catch on whats left of the stripped screw, I just had this problem with my iPhone 4s and it took only minutes to get back on track!
Another perk of doing it this way is that your not making any physical change to the phone itself (e.g. using a Dremel or drill) ((WTF!)) so there is no risk of damaging/scratc
Thanks again...many lessons learned :)