For skill shots, you really just have to practice. If you have a friend who plays or someone who would be willing to help (ask in the DominateDominion chatroom maybe) then you could go into a custom game with someone and play a champ like EZ or someone and just practice landing skillshots in all kinds of situations. Practice is the only real way to get better at them. Also, watch how your opponents move, and try to learn how to predict how they will move when the skill shot would hit them. Path prediction, especially for slower skill shots like anivia's Q is one of the most important things for landing skill shots.
As for knowing when to engage or disengage, well, that is really something that you have to learn with time, as there are many many different situations and rulebreakers that come into play that you need to know. As a general rule though, only engage if it is beneficial to you. Do you outnumber your opponents and is your team in a good position to engage? Then engaging is a good thing (of course only a champ that can engage should, such as a tank). For disengaging, it should be done mostly when you know you are losing a fight, or if the enemy is running from you and there is really no point in chasing them anymore.
For itemization, it really just depends on the game. Adapt your builds to your opponents, and look at Saurons tier list for what items are good. I generally agree with the item list.
Keep in mind that dominion is fast paced. When possible, you want to always be doing something, whether it be ganking bot, defending a turret, getting a health pack, going back to heal and buy, etc.
For chasing and escaping, slows and ms are really good stats. I have found that I love frozen mallet bot for this reason on champs like jax or yorick, and zeal -> triforce is good too.
Here is a link to my guide on dominion that is a work in progress. I hope that if you are up for reading it, then you are helped by it. Also you have perhaps inspired me to write a engaging/disengaging section. https://docs.google.com/document/d/1...XblN94Ul4/edit