"Thanks for helping me" =
Ευχαριστώ που με βοήθησες. (singular) or
Ευχαριστώ που με βοηθήσατε. (Plural) or
Eυχαριστώ για τη βοήθεια.
Another example could be "Thanks for lifting me" which is translated:
Ευχαριστώ που με σήκωσες. (singular) or
Ευχαριστώ που με σηκώσατε. (Plural) or
Eυχαριστώ για το σήκωμα. (not really used)
I would not make any rule about these. The most common way to translate verb + for + ing form in Greek is verb (ευχαριστώ) + που + verb in past tense (βοήθησες) or verb (ευχαριστώ) + για + noun in accusative case (τη βοήθεια). Also I cannot think of an expression using the "by". If you can give me an example, I would be happy to translate it.
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Vasiliki Baskou, Instructor/Director, https://learn-greek-online.com.