I’m going to do that thing again – that thing of encouraging you Latin-Rite Catholics out there to dip your toe into the Eastern Catholic waters.
Not as a tourist, not as an observer at a zoo, but as a Catholic with other Catholics, worshipping God in ancient rites. Yes, it is confusing – even with a book in hand, you are not quite sure where everyone is all the time – but that is part of the fruit, I think. A letting go, a deepening of a sense that something is going on here, something vital and awe-some, even if I cannot fully follow along. For that is what life is. I may want to control it or feel as if I fully, intellectually understand the why’s and what’s of the events in my life and, most importantly, where God is in every iota of it but that’s really too bad, isn’t it?
When we went to the Divine Liturgy at the Byzantine Rite mission in East Tennessee a couple of years ago, Michael remarked that the liturgy raised questions – you leave (if you are unfamiliar with it, I suppose!), wondering what this or that was all about, and it invites you to dig deeper in answer to those questions even as at the same time it invites you to stand humbly, understanding that this is Mystery here, and this is what Mystery is – beyond, yet gracefully here.
Some things I think a Latin Rite Catholic, new to the Eastern Catholic liturgies, might learn or take away:
1) A sense of antiquity and rootedness. Yes, there have been (contested and controversial) changes to one version of the Byzantine Rite liturgy over the past few years (commenters, please add specificity to my vagueness if you like), but for the most part, you are blessedly free from the committee and patched-together yesterday feel that afflicts so much of what we experience in a normal Latin Rite Sunday Mass.
And I’ll note that every Eastern Catholic liturgy I’ve attended so far has been mostly, if not all, in English.
2) An encounter with beautiful, prayerful liturgical traditions – such as that in the Melkite Catholic rite of gathering around, close to the deacon as the Gospel is proclaimed. What is worth thinking about, too, are the times in which we try to do something in the Latin Rite – sometimes it works a bit, other times it doesn’t. Why?
3) Physicality – lots of bowing and kissing of icons and crosses, crossing oneself and so on.
4) Amid the elaborate ritual and lengthy prayers, a relaxed sense of what the congregation does. There is a busy-ness, a looser feel to the congregations at the few Eastern liturgies I have attended. Most people do, indeed, stand when everyone else is standing (which is most of the time) and cross themselves when the Name is mentioned and so on, but not everyone, and there is a lot of coming and going, seemingly random candle-lighting and so on. As well as the fact that hardly anyone was there for the first twenty minutes…
5) The organic integrity of the chanted liturgy. I must say that is attendance at the Eastern Catholic liturgies that helped me understand the concept of “singing the Mass” as opposed to “singing at Mass.” Chant is, I think, the natural language of vocal prayer – not recitation, but chant, even if that chant is nothing more than a sing-song. There was one aspect of this last liturgy that was recited – the prayer before reception of Communion. But that was it.
6) A pretty direct encounter, I think, with the catechetical function of liturgy. Praying the Divine Liturgy, you say two things over and over, in many forms: Lord Have Mercy and God is holy.  In the Latin Rite, we often seem to think that the main catechetical take-away from Mass involves what is said in the homily. But that does not capture it. Then entire liturgy is a moment in time when we worship and we are formed and shaped by the words we say (or chant), the words we hear, the gestures we use and the images that surround us. 
7) An insight, perhaps, even if you have never attended the Extraordinary Form of the Latin Rite, what that is all about. Yes, there is a degree of vocal congregational participation that is not the norm in the EF in most places, but the ancient structure of the iconostasis, the separation of that activity from the congregation, as well as the priest’s prayers offered while the congregation is busily chanting its own thing puts the fearful concept some have of the EF, as they contemplate the inaudible canon or ad orientem or even Communion on the tongue into a broader context of ancient liturgical practices and sensibilities.
It is not all roses, of course.  Life-long Eastern Catholics might have different observations to make – which they have here before – for example that the full-throated congregational participation in chanting the Liturgy I’ve encounter is not universal, and perhaps is not even the norm. The casualness about congregational participation and attendance might cross over into other attitudes towards living the faith. But that’s the way it goes for all of us, Western or Eastern. The Heaven on Earth that graces us in Mass, in the Liturgy, is indeed only a glimpse.
And as in Heaven, there are many rooms. Thank God for all of them!