Make a timeline, in other words start with yourself like this.
Your date of birth/place of birth
sibligs if any dob/pob
parents marriage date and place
siblings if any dob/pob
grandparents marriage date and place
and so on.
Notice where you have blank spaces and put a question mark beside anything you are not sure of. This will help you avoid tracing someone who is not related to you.
Include the origin of your information, for example is it a church or state record.When you have this done, you will be clear about what you have and can depend on and what is a bit shaky and needs further investigation. It will also show you how much you do know already!
Sometimes it is easier to access records/information about a related person who may lead you back to your direct ancestors. Your timeline should also show you this.
This method may take a full evening but you will never regret the time you spend on it and it will save you countless hours down the road.
Never underestimate the value of contacting 'cousins/in-laws' in the country you live in who may have knowledge of family stories unknown to you. Visit if possible, if not write/email/phone. Even if the initial contact is disappointing, sometimes people remember things later.
You may not be able to come up with a place of origin in Ireland for your family initially but you may find a place of origin for a spouse which could lead you back to your direct line. Sometimes people ignore information which they consider immaterial to their search.
In my experience this is a costly mistake (and one which I have made myself!) There are countless stories of people who have found their family of origin by tracing the family of a female spouse, whose place of origin is known, and this leading back to the direct male line.