There are a couple of ways ..
Easiest way is to enable sync'ing with your Google account - Settings .. Google (under Accounts). Tap your google account and then tap Contacts. If you enable sync, this should be kept up-to-date without you doing anything further.
Alternatively, you can export the contacts - Menu .. Import/Export .. Export to storage - then copy the file somewhere safe .. maybe e-mail it to yourself if you don't have a PC.
Failing that, you can sync your contacts with Outlook on a PC - if your phone doesn't come with a PC Sync package that handles this you can get one from the Play Store.
You should also enable Back up my data - Setting .. Backup & reset .. Back up my data. Not sure if that backs up your contacts, but it can't hurt.
