Learn Swedish: Jag börjar att jobba nu. - I am starting to work now.

Because it is in the infinitive (base) form. In Swedish, infinitives usually end in -a. We use this form because it comes after the infinitive marker att (to). You are saying "to work" (att jobba), not "works" (jobbar).

Is att pronounced exactly how it is spelled?

In formal reading, yes, but in everyday spoken Swedish, the infinitive marker att is almost always pronounced as a short "å" sound (like the "aw" in "law"). So you will usually hear natives say "Jag börjar å jobba nu".

The translation says "I am starting", but there is no word for "am". Why?

Swedish does not have a separate grammar form for things happening right now (like the English "-ing" form). The single present tense verb börjar covers both "start" and "am starting". The word nu (now) makes it clear that the action is happening at this exact moment.

Can I skip the word att in this sentence?

Yes, you can! When using verbs like börjar (start), native speakers very often drop the att in everyday speech. Saying Jag börjar jobba nu without it is completely natural and correct grammar.