Learn Finnish: Sanasto kasvaa lukemalla päivittäin. - Vocabulary grows by reading daily.

Lukemalla uses the third infinitive (often called the MA-infinitive) of lukea (to read) in the adessive case (-lla). Adding -malla or -mällä to a verb's strong stem tells you how or by what means an action is achieved. In this sentence, it explains the method by which the vocabulary grows.

How is the word sanasto built?

It comes from the word sana (word). The suffix -sto or -stö is used to form collective nouns, meaning a collection or group of things. Therefore, a collection of words becomes a vocabulary or glossary.

What exactly is the ending on päivittäin?

The suffix -ittäin or -ittäin is added to nouns to describe how often or in what groups something happens. Attached to päivä (day), it creates the adverb päivittäin, meaning "daily" or "day by day". You could also use the phrase joka päivä (every day) instead.

Why isn't there a word for "your" or "my" before sanasto?

Finnish frequently drops pronouns when making general, universal statements. While English speakers often say "your vocabulary" to mean people in general, this Finnish sentence just uses the noun on its own to express that vocabulary in general grows through daily reading.