Seeing how there are lots of stat and build-heavy guides to playing different demigods, I thought I'd make the For Dummies, tips and tricks version. The following tips work well for games against other beginners. Against more experienced players, you are likely to need more survivability items and skills along the way. Anyone have any other tips?
Sedna/Queen of Thorns can summon 4 additional powerful minions. Start by getting the cheapest minotaur and archer idols and a town portal scroll.
Use M to send the minions as a screen in front of the general.
Focus on killing grunts. If you keep your grunts alive and have your minions they can do a lot of damage to demigods trying to chase you.
Your minions give no experience when killed, so don't worry about the enemy levelling by killing unit after unit of them.
When possible, get mana regen % items. Don't get too much of this without buying stronger idols.
If you have a bit of leeway, suppose an enemy demigod has just retreated, you can send simply your hero to capture a flag or return to the item shop whilst your minions keep up the pressure.
Most of the time it is better to hold ground out of enemy tower range and grind xp until you get more abilities, health etc. The archer idol minions have a longer range than towers and can siege them.
General specific:
Queen of Thorns: In closed mode and going straight for Shamblers, Compost and Entourage up to level 10 will make her army have a high ranged DPS. She will be squishy so keep her at the back (good items include +mana %, and +speed to retreat and run around a bit more)
Sedna: Mix up Yetis with healing wind and heal, healing wind works well on choke points and even better when you are working with other generals who are heavy on minions. Pounce allows you to do spike damage whilst Silence can make ability heavy demigods like Torchbearer more manageable.
Oak: If you get the every kill heals chain, focus on making lots of kills to keep your team healed. He's very durable so can hold ground and cover for team members retreating for items/citadel upgrades etc.
Erebus: He gets more minions, the more he (and his minions?) kills. Targetting grunts before demigods then using bite if you've lost a bit of HP is effective. He has drain life and health regen skills as well as Bat Swarm, allowing him to recover from near death states.