I'm not an expert by any means, but here's how I look at it.
Think of the system as having 9 basic parts -- the "in box," and the 8 separate "buckets" that an item from the in box can be processed into, i.e., the trash, reference files, someday/maybe, waiting for, the calendar, the NA list, the projects list, and project support materials.
Some of these buckets depend on others -- i.e., NA's are linked to projects, for example -- but some stand more or less alone, and can be implemented first as a way of building up some momentum.
Taking the parts from easiest to hardest . . .
1. You probably already have a trash can, but you may not use it enough. Get into the habit of trashing anything you don't need or want. You don't need to know anything else about GTD to do this, and it will help clear physical and mental space for the next steps.
2. You probably already have a calendar (if not, get one; if you have two, get rid of one). Start using it for all time-specific tasks -- and nothing else -- and start checking it and using it daily.
3. You may not have A-Z reference files, or if you do, they may not be set up properly. So get the supplies you need and set them up. Start putting things that are not trash and are not tasks, but that you think you may need to refer to later, into your filing system.
None of these 3 steps really requires any detailed understanding of GTD, but I found that these steps alone worked a miracle for getting me organized: throw out trash, file reference materials, and put everything into one calendar.
The remaining buckets are much more interrelated, so you can't really implement them one at a time, but you can work on improving them in stages.
4. Set up your in boxes, and use them. Get into the habit of putting everything that comes into your life into an in box, and then go through the in boxes regularly. Remember, anything that doesn't get routed through an in box will never make it into your system. Notice how relaxing it feels to be able to dump things out of your mind or off of your desk and into your in box, knowing that you trust yourself to come back to it soon. Notice how relaxing it feels to get to the bottom of your in box.
5 & 6. Create project and maybe/someday lists. To me, at least, these are the heart of the system. Projects are the things you are doing in your life; NA's are just "bookmarks" for the next step in those projects (and maybe/someday just holds projects that aren't active). Having a list of projects is like having a list of books that you are reading, while having a list of NA's is like having a list of the page numbers you are on in those books. If you want to read a few pages, you need to know the page number you are at, but if you want a higher level view of what you are actually reading, you need the list of books.
7 & 8. Create NA's and Waiting For lists. NA's are the bookmarks for the tasks you are doing; Waiting For holds bookmarks for the things you have delegated.
9. If you've gotten this far, maintaining project support materials will take care of themselves.
Once you have the system parts all in place, concentrate on doing the weekly review regularly, and use the review to help you identify ways that you can improve or expand (or streamline or simplify) your system.
The next step is to process/store the stuff.