Learn Swedish: Bilen är stor.

Because bilen comes from an en-word (en bil). When you describe a singular en-word, the adjective stays in its base form. If the subject was an ett-word, like ett hus (a house), the adjective would need a -t ending: Huset är stort.

Where is the word for 'the' in this sentence?

In Swedish, 'the' is usually added as an ending to the noun rather than being a separate word before it. The word for 'a car' is en bil. By attaching -en to the end of the word, we get bilen, which means 'the car'.

Is the verb är always pronounced the way it is spelled?

No, in spoken Swedish, är is almost always shortened to sound just like a short English 'e' (like in 'bed'). So you will usually hear people say 'Bilen e stor' in everyday conversation.