As there's no response anymore from the OP, a short summary from the comments for possible solutions:
This issue can have multiple reasons:
- broken/damaged sd card
- trouble with the file system on the card (damaged or simply not existing), or with the partition table
- broken/damaged sd card slot
- incompatible sd card specs (speed, class, brand, ...)
These are the things you should try
Best in the order of their listing:
- Put the card into a card reader, and attach it to your computer. See if it is recognized and readable.
- If it's readable and working fine on the computer, this elmininates reasons 1-2 from above, leaving you with reason 3-4. Continue with 2.
- if the computer claims errors, these are most likely the same keeping the card from working on your Android device. Check what the errors are, and take appropriate actions. Skip to 3.
- Check a different card with your Android device (either you have another one around, or a friend might borrow you one to check with).
- If that card works fine, it eliminates reason #3. As you already eliminated #1 & #2 above, this leaves you with #4 -- Buy a new card (by now you know at least one working brand/class/size combination -- from the card succeeding here), no more checks needed.
- If no other card seems to work, that almost eliminates reason #4 (though you won't be able to check all combinations of brand/class/size, it's unlikely to have tried 5 different combinations and none is working), which leaves you with reason #3 -- a case for the service station. Either get your device repaired, buy a new device, or live without a sd card available.
- If you got here, you obviously have some trouble with the card itself which might be solveable. So here are several things you could try to get it working (again). Consider all data lost which have been on the card (data recovery is a different issue, but if needed, it should take place before you apply any of the below steps!). Stop whenever one of the following steps brought you success:
- Try formatting the card from within your device
- Try the same from the computer
- It might be needed to fix the partitions. With a Custum recovery (e.g. ClockworkMod Recovery) on your device, this can be done from there -- otherwise you might need to do it from your computer. That done, format it again
- check different file systems. FAT16/32 should always work, when in doubt
That should be a nearly complete How-to-fix-It. If I forgot something, feel free to mention it :)
TL;DR -- short variant: