Learn Finnish: Laitan sitruunaa teehen.

Using the partitive sitruunaa means you are putting an unspecified amount of lemon (like a slice or a squeeze of juice) into the tea. If you used the total object form sitruunan, it would mean you are dropping a whole, intact lemon into your cup!

Why do we use the illative case (teehen) instead of the inessive case (teessä) for "in the tea"?

In Finnish, verbs of placing or putting, like laittaa, require the destination to show movement into or onto a place. English says "in the tea", but because the lemon is being moved into the tea, Finnish uses the illative case. Using the static inessive case teessä would sound like the action of putting is taking place while you yourself are already standing inside the tea.

How is the illative ending formed for the word tee?

For short, one-syllable words ending in a long vowel (like tee, maa, or puu), the illative is formed by adding -h, then repeating the vowel, and adding -n. That is why tee becomes teehen.