How do you respond when someone says they are thankful for you?

No response is generally necessary. Depending on the relationship between the two people, a hug, handshake, or simply saying, "thanks", should be sufficient.

On the other hand, if it's something that your spouse or other significant other is saying, you had better be ready to reply with something sincere and loving, and you had better do it immediately. If you had to run to the internet for advice, you're too late.