Like Seriphyn noted, it is worthy to compare the Federation and the Empire. Just like Gallente take it for granted that they have their <insert consumer product and/or service here>, the Amarr have faith. It very likely isn't simply something what secular people (like I assume most of us are) would consider "religion" or being a "practicing believer" - as in, the faith as an action or a statement of something. Rather, for Amarr, "practicing" the faith - perhaps with the exception of some holidays and other "more rare" events - would be as natural as we find having a lunch break.
I think some chronicle or a short story did mention prayer booths - kind of phone booths, except that these have devices that did play back religious material and delivered chemical assistance for getting a religious experience. I'd assume that those would be popular with the busy young upstarts (you know, they were nobodies just three generations ago) in the capital to get the prayer done between making deals at the after-service social event on the morning and heading to the slave market on the afternoon.
The above example also includes the idea of something happening over many generations. I think Paradise is mentioned, so there might be some concept of personal salvation. However, the emphasis clearly is that your acts trickle down to your descendants, so the catch is that if you act well with the system, your children or their children might be better off. Kind of a circle logic there, too - serve well and remember your place and teach your children to do the same, so that their children might, perhaps, raise is status.
Of course, that is only valid for commoners - or only certain facets of the society. It is still completely legal to get rich, possibly even for slaves, as long as you don't try to act against a higher social class. You can enjoy yourself, as long as it is not something differing too much of the norm. The extraordinary example is the Tash-Murkon family. Another example would be the military. It might be, however, that gaining status within a social niche is accepted, and may over the generations even cause social class movement. Military might be the quick way to the top, because a soldier - in fitting conditions - might be able to turn from a private to a general while still staying within the same social niche of "practitioner of the killing profession". Worth to note that I find social discussion perfectly on topic in an Amarr religion thread, since by definition, everything Amarr is religion or religious.
In a way, I assume that the Amarr Empire wouldn't have seemed that strange a few hundred years ago. At least around here, the Church was the institution that took care of things like teaching people to read, recording births, deaths and marriages and so on. There were clearly understood codes, such as a dead person might be clearly identified based on how the church bells rung in his or her memory. The social status directly reflected to worship (with people sitting in the church in places dictated by their social status - and for the better off people in conservative villages/towns, worship would not have been optional unless you wanted the image of a godless outcast).