"I write and then I read."
Translation:Γράφω και μετά διαβάζω.
μετά can mean after, since, then, later, with etc.
Here's a good dictionary link http://www.lexilogos.com/english/greek_dictionary.htm There are also good examples of the various usages.
Here is another link with general help and resources.
Then in this sentence has the meaning of "after", so μετά is correct. Τότε is then when it is used with the meaning of "back then", "at that time", "so". For example: Τότε ήμουν στο σχολείο=I was at school then (back then).
Τότε τι να κάνουμε;=Then (so) what do we do?
Και τότε εμφανίστηκε= And then he appeared (at that time).