A stuck lens cover is a fairly common problem, but it is normally easy to fix. A single grain of sand jamming the cover mechanism is normally the culprit, and you want to try to dislodge it: 1) Try blowing lots of compressed air around the lens cover to clean the mechanism. Or use a hair dryer for a few seconds (don't want to heat up the camera). Use no heat mode if possible. 2) Slide a thin strip of paper between the lens cover shutters and the outer support ring. Work it around 360 degres to clear out any debris that may be in there. 3) With the lens barrel extended and pointed downward, tap the lens barrel with a pencil while you extend and retract the lens by powering the camera on and off. Repeat the above three steps several times. If repeated tries don't work (keeping in mind that it usually does), it then may be necessary to open the lens barrel to access the lens cover mechanism.
You can open the lens barrel up to fiix the covers, but only as a very last resort. The above procedures normally work if you try them enough. But for those particularly nasty stuck mechanisms, here's an example repair
on a Canon Powershot A400 (do this at your own risk, and it will void your warranty).