Hotkeys are detailed in-game. Mouse controls are intuitive.

Some info on basic game mechanics you can find here: http://demigod.wikia.com/wiki/Demigod_Wiki

Skill trees and calculator used to be hosted at DemigodDB, but it's unavailable lately, so you can use this: http://darkwave-studios.com/Demigods/

and this: http://forums.demigodthegame.com/353927 instead.

As far as advanced specific DG-related mechanics go, please refer to guides in stategy section. For example, if you intend to play Sedna, this is a must-read: http://forums.demigodthegame.com/388569

The manual is installed when you install the game.  You can get it here:  C:\Program Files (x86)\Stardock Games\Demigod\bin

or here:  https://www.stardock.com/demigodmanual.pdf

As for a basic tutorial, open www.demigodthegame.com and click on the 2nd video link on the right (the one with the picture of the rook (giant castle guy)).