When I say I’m a semi-reconstructionist, I mean to say that I draw heavily on historical, archaeological and literary sources in building my religious practice but don’t limit myself to those sources.
I’d also like to say that I by no means feel that what I do is the only proper or viable way to honor the gods–we are all different, and different things will work for different people. What works for me is a limited reliance on historical practice to inform my own. Now, a lot of the work has already been done by your co-religionists in terms of working out ritual formats and so forth. There is no pressing need to re-invent the wheel.
But if, like me, you like that sort of thing? It can be a very rewarding way to expand your spiritual life and to personalize your practice.
So, how to go about it?
Finding Academic/Scholarly Resources
There are a few academic books that are generally recommended to new folks, most notably Walter Burkert’s Greek Religion. I’d also recommend anything by Robert Parker and Sarah Iles Johnston, who are both very readable. But where to go from there?
When it comes to determining which sources will be useful for you, the bibliography is your friend. Take any book or article on a subject that interests you–say, votive offerings–and at the end you’ll find a long list of resources that the author of the article found useful in supporting their points. Most of these won’t be useful for you but some will. I recommend keeping a running list of sources to look at and then comparing them, but use whatever research methods work for you.
Locating Academic/Scholarly Resources
It can be hard to find academic sources if you’re not currently enrolled in university. Even if you are fortunate enough to have access to an academic library, you may not have access to the specific sources you’d like if you’re in a different department, or the library may not have them at all–a school that focuses on science and engineering, for example, may well not carry the resources a religious scholar would find useful.
So what can you do?
There are a number of online sources for academic papers. While many if not most are behind a paywall unless you are affiliated with a university that has access, there are a few exceptions.
Academia.edu. Academia.edu is essentially a networking and research-sharing site for academics. While most members are affiliated with universities, the site is also open to independent researchers. Once you sign up, you can follow different researchers or research topics–which means that you can see which of their own papers they’ve uploaded, and read and/or download them. There’s a fair amount of good stuff here and it’s a good way to familiarize yourself with what sort of work is being done and which authors you like. The majority of what is available is current work, and of course it includes only the work of those who want to put it there.
scholar.google.com. Scholar.google.com is exactly what it sounds like–a google search engine for scholarly articles and books. It may or may not lead you to full articles but it will often point you to potential resources. Listings also show how often a given article has been cited by other scholars. I’ve found it most useful in the “looking for where to look for things” sense. 
And if all else fails and I can’t find a piece I really want to read, I have had some luck going to regular old google.com and typing the full title of an article in quotes along with the last name of the author. There are quite a few excellent resources hidden in some odd corners of the internet!
MyJstor. MyJstor is a part of Jstor, a wonderful site with many many journal articles, old and new. Most who use it do so through their university, as individual access to Jstor is not cheap. They do, however, have something called MyJstor, which provides free access to a very limited number of resources. It’s still worth looking into, though, not only for locating those articles you just can’t live without but because of its very nice search function.
Scribd. Surprisingly, I’ve sometimes found the Documents section of Scribd to be a good source of scholarly articles. Scribd is not free but if you already use it, it’s worth looking into.
Determining Which Sources are Good Sources
This is a difficult area even within academia itself. One issue is that in social science (history, archaeology) and humanities (literature) fields, with regard to most topics there are usually several competing theories in play, and even where a consensus has been reached, it can change if the evidence changes. Another is that, as outsiders, it can be hard for us to see which theories are generally accepted and which are way out there.
One cue as to how well a particular source is regarded is how often it has been cited in other publications–which you can find out by searching at scholar.google.com. You can also check to see whether the author has a large body of work, which would indicate some level of success in their field.
One thing to keep in mind is that even when a theory has been found to be faulty, the data on which it is based can still be good and useful (in other words, when the facts are right but the interpretation was wrong, the facts are still right).
The Greek Alphabet
You don’t have to read ancient Greek, but it is helpful to know what the letters are and how they correspond to the modern alphabet. Some authors prefer to spell out some (or, sometimes, most) of the ancient Greek words using their modern letter equivalents, but other authors use the Greek alphabet. This is particularly true of older works, but is also common in articles that draw on linguistic sources and arguments to make their points. I’d suggest, at the least, having a “cheat sheet” of alphabet equivalents to glance at when you’re starting out.
Deciphering the Language
And by “the language” I don’t mean ancient Greek. I mean the specialized vocabulary used in academia. And it’s not an issue of whether you’re smart enough (you are! :)) or educated enough (even someone with an advanced degree wouldn’t have the background to understand scholarly articles in a different field without a little work). It’s an issue of language. Every job has its own very job-specific terminology, and jobs in academia are no different. Much of it, you may be able to pick up from the context. And sometimes the author will specify meaning, particularly when it’s a newer term, one that has changed usage recently, or one that is used in different ways in different contexts or within different areas of study.
Remember that scholarship is secular.
And by that I mean, remember that you are not the audience these pieces were written for. The articles are about religion but they are not religious. Most of the scholars writing about ancient religion are not polytheists or pagans, and sometimes it will be very, very obvious that the authors do not believe in the gods. I personally consider this perspective useful, but it may only be me who finds that to be the case :).
