Learn Russian: Вчера дедушка не брился, потому что он отдыхал. - Yesterday grandfather did not shave, because he was resting.

The ending -ся makes the verb reflexive, meaning the action is done to oneself. The base verb брить means "to shave (someone or something else)", but adding -ся makes it бриться ("to shave oneself"). Here, grandfather is shaving himself.

How do I know whether to use -ся or -сь for past tense reflexive verbs like брился?

It depends on the letter right before it! In the past tense, you form the regular verb first. Since grandfather is masculine, the verb is брил. Because -л is a consonant, we must add -ся to make брился. If the subject were feminine (брила) or plural (брили), the regular verb ends in a vowel, so we would add the shorter -сь to make брилась or брились.

The word дедушка ends in "a". Doesn't that usually mean a word is feminine? Why are the verbs masculine?

You are right that most words ending in -а or -я are feminine. However, words that specifically refer to male family members or men—like дедушка (grandfather), папа (dad), or дядя (uncle)—are exceptions. They are grammatically masculine because they refer to men, so they require masculine verb endings like брился and отдыхал.

The English translation says "was resting", but is отдыхал just the regular past tense?