Although and nevertheless
Obwohl introduces a subordinate clause and moves its finite verb to the end. Trotzdem links a contrasting main clause; when it begins the clause, the finite verb follows immediately.
Understand the idea
Concession presents a result that is unexpected in light of another fact. Obwohl connects the facts with a subordinate clause. Trotzdem expresses nevertheless as an element of a main clause. Similar meaning does not mean identical word order.
Build it step by step
After obwohl, place the finite verb at the end. If that clause comes first, start the following main clause with its finite verb. When trotzdem is first in a main clause, the finite verb follows it directly. Check that the two facts genuinely create a contrast rather than a cause-and-effect relationship.
See it in a sentence
Obwohl es regnet, gehen wir spazieren.
Obwohl er müde ist, arbeitet er weiter.
A useful memory aid
Write the same contrast in both forms. This makes the change in word order more noticeable than studying the connectors separately.
A common trap
Do not put trotzdem into an obwohl-shaped verb-final clause. Also do not leave the subject before the finite verb after sentence-initial trotzdem.