1. Some Templates are simple. Footer Links can be found easily on footer.php ( I assumed you know how to locate your footer.php). Just delete the annoying Links inserted by the Theme Designer.
2. Some Templates are simple but it is coded. Usually Template Designers code their Links, They commonly used based64 encoder to hide their Links. There are two methods to follow.
a. Again, just delete the strange looking contents on the footer.php (cut and paste the deleted contents on a notepad for back up purposes in case failure) and update your theme. Check your website if its fine. If it fails proceed to the second method.
b. You need to decode the strange looking contents using base64 decoder. After you decoded the footer, replace the “coded contents” with the “decoded contents” and delete the undesirable links that you don’t like.
note: If it fails to decode, the designer used other coding method and It wishes you really not to mess with its design.
3. Some Templates are Tricky. Sometimes you can not see any signature links of the designer on footer.php, but instead they hide it inside Theme Functions (functions.php). Look inside functions.php not on footer.php the footer links that you like to be removed and adopt again steps 1 or 2 if you can’t follow.
note: If you are familiar with the famous WP THESIS theme, they used this tactic.
4. Some Footer Links are meant to be there. Designers make it hard for users to remove, If you like their design, they offer you a Fee for the removal of their Signature Links.