Learn Dutch: Kies een boek en lees het verhaal. - Choose a book and read the story.

Because this sentence is giving a command (the imperative mood). In Dutch, just like in English, you simply drop the subject (the "you") when telling someone to do something.

Why do kies and lees come at the very beginning of their phrases?

In command sentences, the verb takes the very first position. We see this twice here: Kies starts the first command, and lees starts the second command immediately after the joining word en (and).

The dictionary verbs are kiezen (to choose) and lezen (to read). Why do their command forms end in -s instead of -z?

To make a command, you use the verb's stem (the ik form). When you remove the -en ending from kiezen and lezen, you are left with a z at the end. However, a strict spelling rule in Dutch is that words can never end in z (or v). Therefore, the z changes to an s, giving us kies and lees.

Why is it het verhaal instead of de verhaal?