From memory the easiest dukedom to play in Ireland is Lienster since it has a decent military and claims on other counties. The best way to get allies is to marry into other dynasties and call them into battle. They'll usually almost always go to war with your enemies if you have a decent relationship with them.
Early game is usually forging decent alliances and building up your buildings in your holdings so you get more troops/income. I would stray away from conquest if you're a "minor power" until you've built up a bit you may even want to wait for a few generations if you just don't have the troops to expand. The AI rarely invests in buildings so you can usually outpace your neighbors extremely quickly with both military and economy.
CKII wiki is a wonderful place to start when you want the basics of the game. Keeping Your Vassals Weak is a must read article, in my opinion.
http://crusaderkings-two.wikia.com/wiki/Category:Beginner%27s_GuideIreland is my preferred recommendation for newbies since the Isle is mono-culture and mono-religious. That makes expansion much easier and there much less penalties for occupation. It's easy to go from a count to duke to king and experience the basics of each, later the Empire of the British Isles could be formed. Ireland is rarely a target for conquest from any other country since England, Norway and Scotland will be busy fighting civil wars and culture shifts. Ireland can also expand into Wales and Brittany extremely easy and with the aid of a few mercs and holy orders can even win the crusades and claim the Holy Lands! Now that's Irish Piety.