Try restoring from backup, but that may not work. iTunes backups are unreliable for contact info. If you used iCloud for your Contacts, you may get it back that way, but I've found it a bit unreliable. You need to get a contact app for your computer. If you don't have Outlook, and don't want to buy it, google for contact apps that fit your budget and your needs.
Another easy way to get your contacts back:
Go to your mail settings -> icloud and turn off contacts. Your contacts should now be visible again. Note that in most cases, the contacts are not actually missing. It's just that the contacts list has an issue where it seems to have trouble displaying the contacts when multiple lists are active. Once your contacts are back, you can turn icloud contacts back on and re-merge them. Note that when you turn it off, it will give you the option to keep or delete contacts on your phone - click KEEP!