Progressive Form

In English, the progressive form refers to our -ing verbs, and it shows that something is in an ongoing state. "He is running" tells me that the action is currently happening. There's an equivalent version in Japanese used with the ている form of verbs.

This simply requires putting the verb in て form, then adding いる to the end of it in its appropriate form. It can be conjugated as necessary as a standard ichidan verb, so います, いない, etc. The tense is determined by how いる is conjugated.

アヤトは本を読んでいる。
Ayato is reading a book.

ライトは今寝ていない。
Laito is not sleeping right now.

スバル君はお菓子を食べていた。
Subaru was eating candy.

This is actually very similar to the construct we use in English and thus fairly easy to read. In more casual situations, the い in いる is dropped, so it'll read as てる (or the appropriate conjugation, minus the い).

何をしてるの？
What are you doing?

リーさんに話してるよ。
I'm talking to Lee-san.

今テレビを見てない。
I'm not watching TV right now.