Learn Russian: Я сейчас отдыхаю, а ты работаешь.

Because the subject is я (I). To make this form, we take the dictionary form отдыхать (to rest), drop the final -ть, and add -ю. This is the standard pattern for first conjugation verbs when talking about yourself.

What happens to the verb работать when it matches ты?

Just like the first verb, we drop the -ть from работать (to work) and add the ending -ешь to match ты (you, informal). So we get работаешь. Make sure not to forget the soft sign (ь) at the very end when writing it!

Why does the sentence use а for 'and' instead of и?

The word а is a contrastive conjunction. It is used here to contrast two subjects doing two different things (I am doing this, whereas you are doing that). If you used и, it would sound strange, like a simple list rather than highlighting the difference between my resting and your working.

How do you know it means 'I am resting' rather than just 'I rest'?

Russian doesn't have a separate 'present continuous' tense with 'to be' and '-ing' words like English does. A single present tense verb like отдыхаю covers both 'I rest' and 'I am resting'. Here, the word сейчас (now) makes it clear that the resting is happening right at this moment.