It comes down to personal preference, but it's quite common to echo the sentiment back to the person. For example.
A: Happy Holidays!
B: Thank you. Happy Holidays to you too!
It's also quite common to hear more informal responses, such as:
- "And (also) to you!"
- You too!
- Thanks, same to you!
- Happy New Year to you and yours (when you want to extend the wishes to the other person's family)
"Many happy returns" (although primarily used nowadays to mark a birthday), as also an acceptable response to "Merry Christmas" and "Happy New Year". The sentiment itself is issued the hope that a happy day being marked would recur many more times.