thereby/hereby

My advice: don't use the words "thereby" or "hereby".

The word "hereby" means "here in this document", and is typically only used in legal statements in the phrase "I hereby declare..."

For example:

I hereby declare that I, John Smith, agree to to terms of this contract.
I hereby declare that Bob Jones worked in my company from January to October 2010.


The world "thereby" means "doing that made something happen".

For example:

She dropped her cup on the floor, thereby causing a disruption to the classroom.

http://simple.wiktionary.org/wiki/thereby


Origin of the confusion:

In German there are two words, "hierdurch"/"hierbei" and "dadurch"/"dabei" that are very similar to "hereby" and "thereby". One big difference is that "hereby" is not used outside of legal documents. The other big difference is that "thereby" can not be used at the start of a sentence, and that you need a comma before and an -ing verb after "thereby" (see examples above).

Here is the correct way to translate "hierbei"/"hierdurch"/"dadurch"/"dabei"

Prozess X ist blabla und ist ein wichtiger Teil von Y. Hierbei wird ABC gebildet und bla bla.
This would be translated as :
Process X is blah blah and is an important part of Y. During this process, ABC is formed and blah blah...  or
Process X is blah blah and is an important part of Y. ABC is formed during this process and blah blah...

Prozess X ist blabla und steigert den Y-Wert. Dadurch wird weniger ABC gebildet...
This would be translated as:
Process X is blah blah and increased the y value. This means that less ABC is formed...