Learn French: Tu devrais éteindre le chauffage avant de dormir. - You should turn off the heating before sleeping.

We use avant de followed by the infinitive (dormir) because the subject doing both actions is the same (it is tu turning off the heating and tu going to sleep). If the person sleeping were someone else, you would use avant que followed by a conjugated verb.

Why is the verb devrais in the conditional here instead of the present tense?

The verb devoir means 'must' or 'to have to' in the present tense (tu dois = you must). When you want to soften it to give advice—saying 'you should' instead of 'you must'—you use the conditional form: tu devrais.

If I wanted to reverse the sentence and say 'before turning off', would it be avant de éteindre?

Almost, but you must drop the 'e' in de and add an apostrophe because éteindre starts with a vowel. It becomes avant d'éteindre.

I know éteindre means 'to turn off', but what is the verb to turn the heating 'on'?

The opposite of éteindre is allumer (to turn on or to light). To tell someone to turn on the heat, you would say allumer le chauffage.