Do is for activities and obligations
"Do" pairs with unspecified tasks, chores and duties: do homework, do the dishes, do a favour, do business, do your best, do exercise. Notice these are often things without a concrete, created result — you don''t end up holding a physical "homework".
Make is for creation and results
"Make" pairs with things you produce, decisions, and communication: make a decision, make an appointment, make progress, make a mistake, make a suggestion, make money, make a phone call. These usually end with something new existing — a decision, an appointment, a mistake.
The exceptions to just memorise
A handful of fixed phrases don''t follow the pattern and simply need to be learned as whole chunks: make sense, make friends, make an effort, do research, do a good job, do harm. Write these six on a card and drill them separately from the general rule.
Practice
Take the last five emails or messages you wrote. Find every "make" or "do" and check whether the surrounding phrase matches the pattern above or is one of the fixed exceptions.