Learn Hardcore Icelandic: Lestu textann upphátt, vinsamlegast.

Lestu is the singular imperative form of the verb lesa (to read). It is the form you use when telling one person to do something: Read!

In this sentence, Lestu means Read as a command or request directed at one person.

The -tu ending is a common imperative pattern in Icelandic for many verbs when speaking to you singular.

Why does the sentence use Lestu instead of something like þú lest?

Þú lest means you read or you are reading in a normal statement, not a command.

Compare:

Þú lest textann. = You read the text.
Lestu textann. = Read the text.

So Lestu is specifically the command form, while þú lest is a present-tense statement.

Why is there no word for you in the sentence?

In Icelandic, the subject pronoun is usually left out in commands, just like in English:

Read the text.
Lestu textann.

You can add þú for emphasis in some contexts, but normally it is unnecessary. The verb form already shows that the speaker is addressing one person.