There is not tutorial for the game. If you have played DotA the concept is fairly similar. If not just do a few skirmishes against AI and you'll get the hang of it pretty quickly. Once you get a little confidence increase the number if AI opponents and/or difficulty.
You should develop some stratagies for the beginning of the matches for each Demigod you like to play (item purchases, skill selection and progression, etc.). You will eventually figure out what works best. Best advise I can give as far as items go is you'll want to purchase the banded armor and/or scaled helm right off the bat. Also, don't understimate the power of teleport scrolls, they will save you precious time moving around the map and porting back to base to heal up.
As far as gameplay goes, learn to push with your creep (your mobs). Over-extending your creep can be deadly, especially in the beginning of the game. If you are below lvl 7 or 8 and you find yourself next to a tower... RUN! you can't take it out yet and you don't have the HP to loligag around.
The primary goal is to hold the flags (each flag gives you different bonuses to you and your creep). By holding flags you generate war points which add to your war score. Increasing your war score allows you to purchase upgrades at your citadel that will benefit/upgrade your structures and your units. Overpowering the enemy units is key to pushing through their base.
Keep in mind... being killed by enemy Demigods "feed" them (gives them lots of experience and money). Learn the enemy's skills and know when it's time to retreat. Getting killed multiple times in the beginning parts of the game will usually decide the outcome. Going back to base to heal up is nowhere near as detremental as getting squished.
Good luck!
-AMC