How do I save my contacts from my iPhone to my computer?

Are you on a Mac or PC?

If you are using iCloud you can just turn on iCloud syncing (Settings>iCloud>Contacts>On) and your contacts will be backed up in iCloud. You could also use an app like My Contacts Backup, which will back up your contacts as an attachment to an email that you send to yourself for safekeeping. If necessary, you can open this email later and tap the attachment to re-import the contacts back to your phone.

(iTunes provides the ability to sync contacts to a supported program on your computer such as Outlook, however it is sometimes difficult to begin syncing contacts if you have already been syncing with iTunes on your computer. It's also possible to accidentally delete the contacts on your phone when you try. If you want to try anyway, first back up your contacts using My Contacts Backup in case something goes wrong. Then you must first enter at least one contact in the program you will be syncing your contacts with prior to syncing. Then connect your phone, go to the Info tab of your iTunes sync settings and select Sync Contacts. When you sync you should get a merge or replace prompt for contacts; choose merge. If you don't get this prompt and your contacts are deleted from your phone, use the My Contacts Backup email to re-import them to your phone.)