A bulb just went out and you don't feel like going to the store and getting a replacement. No problem! Believe it or not, some can be fixed REALLY easily and keep going for another year even! It only takes a minute too and anyone can do it without any tools or anything.
First you should know that this stands almost no chance of working with a frosted bulb. It has to be 100% clear so you can see what you're doing. Start by taking the bulb out of the socket with the light switch or lamp turned off.
Next, examine the tiny, springy filament that's held between the two metal poles. It should be noticeably broken. If the filament broke and curled over itself, sorry but you're out of luck. It's extremely unlikely to unhook from the position and you need it to. If the break is pretty much anywhere else, you should be able to fix it.
The whole fix is basically to get the filament re-connected. Some part of it melted and broke but if you reconnect it in another spot, you've got a complete circuit again. If the filament is broken near the middle and there's two springy pieces sticking off of each metal pole, it's really simple to fix it. Hold the base between your hands and move them forward and backward to spin the bulb rapidly. The filament pieces will stretch and wave around wildly and after a short time, they should catch on each other and tada, it's fixed.
If the filament is mostly broken on one side or another, you should first try the technique in part 3. If that fails though, try holding it by the base with the broken filament facing forward towards the metal pole it needs to connect to. After that, pitch it like a baseball except DON'T LET GO! Just stop abruptly at the end of the pitch so the springy filament stretches out and hopefully latches onto the metal pole or any tiny filament remnant on that end.
If all else fails, try some other logical movement to hook the filament back up. Just be very careful not to hook the filament up to itself because it's unlikely to unhook.