1. Explain it simply
虽然 opens the first clause ('although'); 但是 opens the second clause ('but').
Chinese keeps BOTH words, even though English drops the 'but'.
虽然 comes first and 但是 comes second, so never swap them or move either one into the other clause.
2. Show examples
虽然天气很冷，但是我想去跑步。
Suīrán tiānqì hěn lěng, dànshì wǒ xiǎng qù pǎobù.
Although the weather is cold, I want to go running.
keep both words
虽然这件衣服很贵，但是我很喜欢。
Suīrán zhè jiàn yīfu hěn guì, dànshì wǒ hěn xǐhuan.
Although these clothes are expensive, I like them a lot.
但是 = but
虽然商店很远，但是东西很便宜。
Suīrán shāngdiàn hěn yuǎn, dànshì dōngxi hěn piányi.
Although the store is far, the things are cheap.
contrast
虽然我很忙，但是我还想去玩儿。
Suīrán wǒ hěn máng, dànshì wǒ hái xiǎng qù wánr.
Although I'm busy, I still want to go out and play.
paired
3. Share a tip
Keep BOTH words: put 虽然 in the first clause and 但是 in the second. Unlike English, Chinese never drops the 'but', and you must never swap their order.