Journals, conferences, lectures, and blogs.
Each subfield of history has a few journals that are generally recognized as containing the latest and best research. In early medieval history / archaeology these include Early Medieval Europe, Medieval Archaeology, and the Journal of Late Antiquity. For the middle ages in general, the biggest journal is the rather unfortunately named Speculum (it's latin for mirror, ok!). The best Marxist / materialist history from all fields / time periods is often published in Past and Present. You can stay on top of the latest published and peer-reviewed work in the areas of history that you find particularly interesting by identifying and following the leading journals in which this kind of history is published. If you want help figuring out which journals this might be, you can ask us and we'd be happy to make some suggestions.
In addition to the latest articles, these journals will also publish reviews (by academics) of recent books, and this is a great way to see which books might be worth interlibrary loaning or purchasing. All academics have a few journals that they keep tabs on to stay up-to-date.
How do you access these journals? The best way is through a database like jstor, which hosts the contents of hundreds of journals. All university libraries, and some public libraries, have access to these databases (your local library might have one). You can also, however, subscribe to specific journals for an annual fee. Sometimes these fees are reasonable, other times their ridiculously overpriced; it depends on the journal.
That's peer reviewed, published articles. But the process of peer review takes time, and publication can take longer. In the sciences, turnover is quick, but history papers can sometimes lag for years between writing and publication. That means that just reading journals won't always keep you on the very front edge of knowledge. To do that, you need to interact with historians who are in the process of developing and testing their new ideas.
The best way to do this, in a generalized way, is to go to conferences. Conferences are aimed at academics, but are usually open to the public (sometimes, you have to pay a registration fee, other times you don't - depends on the conference). At conferences, academics present short versions of their latest research and receive questions and comments from the audience. Then they get drunk and talk about it all together. Most conferences are good fun, both intellectually and otherwise.
There are huge national conferences that cover everything, the biggest being the AHA which happens every year just after new years. For medieval studies, there's Kalamazoo, a conference that attracts thousands of scholars interested in all parts of the middle ages. But the best conferences are usually the smaller ones that focus on a specific theme, and they're hosted all the time all over the country. If you have a budget and like talking to people, they're a great way to hear what's going on.
Conferences require time and travel, and you always end up hearing a mix of great, good, and ok papers. If you want to be more focused, or have less time, you can have good luck attending lecture series hosted by your local university history departments. Like conferences, these lectures usually focus on new, not-yet-published (or only just published) research, and can be a great way to get a sense of what people are working on right now. I just went to a lecture about a yet-to-be-published archaeological site, and walked away with a much better idea of what they're found and how they're studying it, and a ton of new ideas for my own understanding of the period. If you're close to a university, see what they have going on.
Finally, there are blogs. A lot of historians are moving some of their work online, and no matter what parts of history interest you most, there are probably a few leading scholars sharing regular posts and updates online. These will be less intense and scholarly than journal articles of conferences, and yet still communicate the latest questions, controversies, and movements within the specialists' fields. I follow a few scholars, like Guy Halsall's blog about late antiquity (and various other entertaining rants), and Howard Williams' blog about death and memory in early medieval England. We can probably recommend some good scholars who write about your particular areas of interest.