The best time to buy is when the price is lowest for the route you want. Unfortunately, none of us know when that is. The airlines use computers to change fares many times a day, and there simply is no rhyme or reason any more.
Concrete example: a month ago I was looking at airfares for mid-May from New York (so, two months out - in theory, too close to travel to get any real bargains). The cheapest flights to Europe I found were to Zurich, nonstop on American or Delta - $349 (not a typo - three hundred and forty-nine dollars!). As a friend pointed out, taxes alone on some flights are nearly that high. Then I looked at Geneva for the same dates. Nonstop flights were about $1200, and one-stop flights started at about $650; it was about $700 for flights that didn't have a very long layover in Casablanca (yes really - Royal Air Maroc was having a sale).
So, why was Geneva double to triple the price of Zurich? Why was Zurich so cheap for those days? Who knows?
So, start looking immediately to learn who flies from Houston to Dublin and the connections involved. Are you sure you want a round trip - many people start in Dublin and end in Shannon to avoid backtracking. To find these flights, use the "multi city" or multiple destinations" option of Kayak or Google Flights. Also check the websites of the airlines themselves.
Having done this research, you'll see what the current airfares are, and will figure out which routes you'd prefer. You'll then be able to spot a better fare on a route you want, and POUNCE; be ready to buy right away if you see a good deal, as these sometimes evaporate quickly.