An IMSI is usually 15 digits long, but can be one or two digits shorter.
Now you have your IMSI number you'll need the authentication key (Ki), which is unique to your SIM. This number can only be discovered electronically using a SIM duplicator, which is an external device that you will slot the SIM card into.
A SIM duplicator is relatively inexpensive - they can be found at around the $10 mark - and can be purchased at multiple locations. A Google search for 'Super SIM' will turn up at least several online outlets.
When the SIM duplicator is connected to your PC and your SIM card, it will attempt to acquire the Ki number and copy the entire contents. When a new SIM card is placed into the duplicator after this process is complete, that data will be copied and, for all intents and purposes, the new SIM will be identical to the old