Welcome to the forum, Wheelbarrow,
One of these days, we'll likely concoct some quick and easy way to point inquirers, such as yourself, to lists of reference materials that members have compiled in response to this same inquiry. However, the advantages of doing so aside, it would lack the human touch which invariably offers new ideas to supplement the well-worn and treasured recommendations that are repeated time and again - and would deprive newcomers of an opportunity to interact with and get to know some of us as individuals (for better or worse

).
As you might guess, the question has been asked and answered a whole bunch of times, but it isn't a topic that easily lends itself to a quick search of the site and retrieval of threads with the relevant information. So, patience, and answers will be forthcoming.
From your post, I'm guessing that you are interested in coming to a better, fuller understanding of Eastern Christian theology and spirituality, as well as learning about our liturgical forms. (History is another whole thing, but generally more easily found - albeit accurate history might require a bit more of a search.) It's a very late hour (and I'm beat) but I'll offer a few quick suggestions, knowing from experience that my brothers and sisters will flesh these out.
A caution, at the outset: be prepared to find that some of the most strongly recommended texts on theology and spirituality will be by Orthodox writers, as our (Eastern Christian - Orthodox and Catholic) theological and spiritual roots are generally one, albeit some doctrinal differences are among the factors that prevent us from being one in the Mysteries.
There are two authors, one Catholic and one Orthodox, whose writings offer an incredible wealth of information on Eastern spirituality and theology in the Byzantine tradition. They are Archbishop Joseph Raya, of blessed memory, and Metropolitan Kallistos Ware. Both are eminently readable authors and their writings will enrich your knowledge immeasureably.
Another wonderful resource is
101 Questions and Answers on Eastern Catholic Churches by Deacon Ed Faulk, a friend and fellow forum member. It is geared toward Latin Catholics and intended to provide an overview of theology, praxis, and structure in the Eastern Churches - highlighting differences and similarities. Although the focus is on the Byzantine Rite Churches, it includes references to all of those in the Eastern and Oriental Communion.
As far as becoming familiar with liturgical practices, some of the very best material is available on-line. Khouria Frederica Mathewes-Green's essay
12 Things I Wish I'd Known ... First Visit to an Orthodox Church [frederica.com] is a classic primer what to expect on the occasion of one's first entry to an Eastern temple - and its wisdom applies equally to Eastern Catholicism as it does to Orthodoxy.
The website of St Elias Ukrainian Greek-Catholic Church [saintelias.com] (Brampton, Ontario, Canada) is another place online to obtain a wonderful overview. Its tab on Church Etiquette is an incredible resource for those coming East for the first time.
Hopefully, those ideas will get you started. My brothers and sisters will quickly add their suggestions. Again, welcome to the East and to the forum.
And, btw, should you need directions to get to the only Eastern Catholic parish in Ireland, we're honored to have its pastor, Father Serge Keleher, among our members here.
Many years,
Neil