Hi Mary, and welcome to AF
How may depend on what phone you have. We have forums here for most android phones, so you should visit yours to find out more. Some manufacturers have software for syncing with a PC. There are also third party applications for synching android with a PC: I've heard the name MyPhoneExplorer, but have never used such a program.
You can automatically back up your contacts to your gmail account. Indeed if you store them on your phone as google contacts and have sync enabled on the phone you may already have done so! To check, log on to your GMail from a browser, click on the red word GMail and select "Contacts". They may already be there.
One final option is to go into the Contacts app on your phone, and select import/export in the menu and export them to your SD card. This will back up your address book as a vcard file (.vcf), which you can copy to your PC for a backup or import into your favourite contacts program on the PC. You can also import contacts to the phone in the same way.
Hope one of those options works for you, and that you enjoy the forum