Look my love; It depends on the type of mobile you have..
In some mobiles you can take the memory out and connect it to your laptop or pc and do the copy, if you have e-mail service in your mobile you can e-mail your self with the phone book.. if non of the above is possible; take sit down and type them!;-)
Depending on your Phone you may be able to buy a data cable, or even better you may already have one with your phone purchase, along with some software. if you do install and set this up.
Failing this, purchase a Mobile Sim reader, you can plug this into your PC, and it reads the SIM Data, to allow you to modify it, and back it up, so if you lose it, you can simply insert the new SIM and write the backup to it.