Text selection via the keyboard is achieved as in most text editors - and usually involves using the cursor keys together with the Shift key. In particular:
Shift+DownArrow will select the current line.
Shift+RightArrow will will increase the text selection by one character.
Shift+End will select to the end of the current line
Shift+PageDown will select an entire "page" of text
Selected Text and Scrolling
Unlike most text editors, V does not clear any selected text when the keyboard is used for scrolling. That is, as you scroll the file with the arrow keys, any selected text remains selected. The selected text will remain selected until you either start a new text selection or you left-click on the file with the mouse.
The selected text can also be cleared by pressing the key associated with the Clear Selected Text command. There is no default keyboard shortcut to do this, but you can customize the keyboard to assign a key to Clear Selected Text (which is in the Other submenu of FILE).