Learn Swedish: Jag var ledig från jobbet.

No, it stays exactly the same! var is the past tense of vara (to be). Unlike English, which switches between 'was' and 'were', Swedish verbs in the past tense do not change based on who is doing the action. You will say jag var (I was), du var (you were), and vi var (we were).

Does ledig mean 'free' like a product that costs zero money?

No, ledig specifically means 'free' in the sense of having time off, not working, or being unoccupied (like an empty seat). If you want to say something costs no money, you must use the word gratis.

Why is there an '-et' at the end of jobbet?

jobbet is the definite form, meaning 'the job' or 'the work'. In Swedish, you do not use a separate word for 'the' but instead add it to the end of the noun. Because jobb is an 'ett' word (ett jobb), it takes the ending -et to become jobbet.

Do I always need to include från when using ledig?

You only need från (from) when you want to specify exactly what you are taking time off from, such as jobbet (the job) or skolan (the school). If it is already obvious from the conversation, you can simply say jag var ledig (I was off).