Your contacts and text messages stored in the SIM can be recovered, transferred, edited or backed up with a SIM card reader, available online, and a PC. The SIM card reader is a USB device. Be sure to get one that comes with PC software. Install the software, put your SIM in the reader, enter your PIN code (the same one you use to unlock your cell phone) and you have access to your contacts and text messages like any files on your PC. This will not give you any other information, however, such as your subscriber information, pictures or music. If you never used your cell phone PIN code or didn't even know you had one, call your phone company and they can probably tell you what it was.
Two other options to access information from your SIM are to connect your cell phone to a PC with either USB or Bluetooth, which also lets you save your media files, or to get a backup service from your cell phone company, who can help you do all of these things at their store.