Like others have said, stack health/regen, know when to retreat, practice against the Hard AI, read the strategy guides, etc. I would also add that you should try to master 1 or 2 demigods at a time and learn what they are best at. When I first started, my biggest problem was that I didn't use my level-up points well. I would just spend them on the next thing available in the skill tree; I didn't know that you could save them until something that you really liked became available. Also, I didn't tailor my item purchases to either my strategy or my chosen abilities. Thus, I was just building demigods that could do a little of everything, but nothing particularly well.
I would suggest first determining how you want to play and what kind of contribution you want to make to your team. I play Lord Erebus sometimes, and I like to build him as a fast-strike assassin, with a small entourage of idols and minions. So, I get Blood of the Fallen as a favor item; build up Bite, Bat Swarm, Coven, and Improved Conversion; and upgrade health, armor, and regen items as I can afford them (also, buy at least one good mana item like the Veloth helm). You can play LB as strictly a high-hitpoint, demigod-killing assassin by skipping the minion abilities and idols and just buying buffing items and investing in a stunning ability like Mass Charm, along with Bite, Bat Swarm, etc. Also, you can build him as anti-infantry by investing heavily in Mist and mana items--there is a build that can allow you to stay in mist form for a long time and just own a lane of creeps. It all depends on whether you want to play as a minion-leading general, a demigod-killer, an anti-infantry Mist demon, etc.
Just pick a demigod that you like and practice builds against the AI. There are a few viable options for most of the demigods. You like Oak and Rook; both have a few different builds that can help win a game. Rook can be a tank, has strong anti-structure abilities, can control a lane with towers and hammer smash, and is an effective demigod-killer if you stack health, regen, and damage items and abilities. Oak is one of the most versatile demigods in the game and can easily be played as a solid assassin or general. Just try to choose a build that fits the map, helps your team, and maximizes your demigod's native strengths. Avoid trying to build a do-it-all demigod. Instead, determine his/her role in the game and then customize accordingly.
Good luck to you and have fun.