Try to clean the contacts of the Sim card, and if you can, the sim card reader.
The Sim Card it self can be cleaned with a clean pencil eraser, using a light rubbing action. This would get off any dirt or oxidation.
You can also use rubbing alcohol on a cotton swab or q-tip to clean the contacts.
The sin card port/ reader it self, is a slightly different matter, if you can clearly see the contacts and reach them just fine, the process above would work. You can also try some compress air to blow out any dirt or foreign objects.
If none above works (last resort measure since this will void your warranty), you might have to disassemble your iPhone.