Learn Finnish: Laulava lintu istuu vihreässä ruohossa. - The singing bird sits in the green grass.

It uses the active present participle ending -va. You take the strong verb stem (laula-) and add -va (or -vä depending on vowel harmony) to turn the verb into an adjective. Here, it means "singing" or "the one that is singing".

Does the participle laulava have to match the case of the noun lintu?

Yes! Because laulava acts as an adjective modifying lintu, they must be in the same case. Here, both are in the basic nominative case. If the sentence was "I watch the singing bird" (Minä katselen laulavaa lintua), both words would take the partitive case ending.

Could I say Lintu, joka laulaa instead of Laulava lintu?

Absolutely. Laulava lintu (the singing bird) and Lintu, joka laulaa (the bird that sings) mean exactly the same thing. Finnish uses these -va/-vä participles a lot to make sentences more compact.

Why does the ending for "in" look different in vihreässä compared to ruohossa?

This is a classic example of vowel harmony. The adjective vihreä has front vowels (e, ä), so it takes the front-vowel version of the inessive ending (-ssä). The noun ruoho has back vowels (u, o), so it takes the back-vowel version (-ssa). Even though adjectives and nouns must agree in case, they apply their own vowel harmony rules to the suffix.