1. Explain it simply
虽然 introduces a fact; 但是 introduces a result that goes the other way.
This means 'although...', so the two halves contrast.
虽然 pairs with 但是, not with 而且 or 就.
虽然 can sit before or after the subject; 但是 starts the second clause.
2. Show examples
虽然我很累，但是我很开心。
Suīrán wǒ hěn lèi, dànshì wǒ hěn kāixīn.
Although I'm tired, I'm very happy.
the two halves contrast
虽然今天下雨，但是我还想去。
Suīrán jīntiān xiàyǔ, dànshì wǒ hái xiǎng qù.
Although it's raining today, I still want to go.
虽然 A，但是 B
虽然他很年轻，但是很努力。
Suīrán tā hěn niánqīng, dànshì hěn nǔlì.
Although he is young, he is very hardworking.
但是 starts the result
3. Share a tip
虽然 pairs with 但是, not 而且. Put 但是 at the start of the second clause (但是我很开心), and make sure the second half truly contrasts with the first.