Mmm. Perhaps I could add some antiharassment tactics? Slightly off-topic, I know, but new players who read about harassing and now understand it (Yay, knowledge!) should also know ways to mitigate it.
First and foremost, if you find a demigod is simply beyond your skill level/a powerful counter to yours, feel free to ask for a lane-switch. Nobody on the team is done a favor when a teammate cannot control his lane.
Keep an eye on your minimap! The 'gank' tactic Zeh mentioned above me can easily be avoided against most oppenents; if an enemy player is missing for more than 30 seconds, chances are he isn't just taking a trip to the fountain.
In DotA (not sure whether it's popular in Demigod), players who are gone for a bit are called "MIA" by the person in their lane. This allows smart players to know when danger is lurking.
Finally, it is usually most effective to start with skills that offer good harassment (Fireball, spit, rain of ice, etc) in the very early levels, as most AoE's will lack the punch and mana-efficiency to net kills. Keeping your opponent harassed not only slows her farming down to a minimum, but also decreases the liklihood that she will be willing to risk going toe-to-toe with you. And that means more creep kills and money!
Happy Gaming!