Modal clauses are subordinate clauses that answer the question "how?"
In German, the questions words are: "Wie?" "Wodurch?" "Auf welche Art und Weise?"
Modal clauses start with the conjunctions "indem" or "dadurch / ohne / anstatt dass…" You can also use the infinitive phrases "ohne… zu…" and "anstatt… zu…"
"Indem" and "dadurch dass" explain exactly how the goal was reached.
Wie / wodurch / auf welche Art und Weiße kann man Millionär werden?
What’s the goal? → How do I reach that goal?
"Dadurch dass" can be separated like "so dass" (Consecutive Clauses). When doing this, the main clause MUST come first, and "dadurch" comes before the goal / result.
"Ohne dass" and "ohne… zu" express what was not done.
"Ohne dass" is a normal subordinate clause (verb at the end!) and "ohne… zu…" is an infinitive construction.
"Ohne… zu…" can only be used when the subject is obvious (i.e. the same as in the main clause). You can read more about infinitive constructions in general here.
"Anstatt dass" and "anstatt… zu…" describe a potential alternative that is NOT being done.
"Anstatt dass" is a normal subordinate clause (verb at the end!) and "anstatt… zu…" is an infinitive construction.
= „Ich schwimme im Pool und nicht im Meer.“
"Anstatt… zu…" can only be used when the subject is clear from the context.
"Indem," "dadurch dass," and "ohne/anstatt dass" are used at the beginning of subordinate clauses. That means the verb goes at the end.
"Ohne/anstatt… zu…" are infinitive constructions. That means "ohne" / "anstatt" goes after the comma and the zu + infinitive goes at the end.
An overview of subordinate clauses.