Q: how   to  update  iphone  3gs.(factory  locked)

If your phone is not officially unlocked by the provider, it will probably be locked again after the iOS update, if you can get it to register again after the update.

Unauthorized modification of iOS has been a major source of instability, disruption of services, and other issues

If your phone has been officially unlocked, follow this article to update:

iOS 4: Updating your device to iOS 5 or later

Check if the provider to which the phone is locked to offers unlocking:

iPhone: Wireless carrier support and features

Follow these instructions to unlock your iPhone:

1. Check if your carrier offers unlocking. Only your carrier can unlock your iPhone.
2. Contact your carrier and request an unlock.
   • You may need to meet certain requirements to qualify for unlocking. This may take up to seven days.
3. Once you receive confirmation that your iPhone unlock has been processed, back up your iPhone.
4. Erase the contents of your iPhone.
5. Complete the setup assistant and restore your backup.

copied from iPhone: About unlocking

Hard to say, as your provider may have different options included in your contract.

Contact your provider to find out, click on the blue link to see if your carrier offers unlocking:

iPhone: Wireless carrier support and features