Crack a history book. I recommend The Collapse and Recovery of the Roman Empire by Michael Grant. It's relatively short, and if you know a good deal about the Empire of Augustus, it's a great way to see how the Crisis of the Third Century totally changed the situation within the Empire.
You can supplement that with a good book on daily life in the Empire. There are tons, and some are very accessible. Daily Life in Ancient Rome by Jerome Carcopino should be more or less available and useful for you.
I'm currently running a fantastical Iron Heroes game set during the Crisis of the Third Century, but I've got a pretty good background in history, so I don't do a lot of research for each game other than some Wikipedia browsing. I'm not intent on 100% accuracy either, just a good feel.
And honestly, you don't need that much knowledge to pull it off. Just know more than your players and plan your adventures well so you know exactly what historical tidbits you're going to throw in where.
Note, I just checked on prices to provide a link, but Amazon has it listed for $80.00. That's crazy. I picked it up for $5.98 at my local Half-Price Books. I'd recommend buying one of the used copies through Amazon for cheap.