It doesn't matter what time period you're portraying; staying "in character" and never mentioning cell phones, computers, on any other 21st century amenity is hard. So how do you know how to watch what you say and actually act as though you're a person from another era? It's easy if you keep a few simple rules in mind.
(1) Study the time period you are portraying. Study so hard that you think, feel, and breathe that era. Learn what people ate, how they talked, and what they wore. Acquire a liking for fried eel, poached quail, or any other historical favorite that may no longer be on the menu (okay, you don't have to go *that* far). Find out what people knew of geography at the time; it's hardly appropriate to be talking about the Australian
Aborigines if you're portraying a man or woman from the Middle Ages.
(2) Dress the part. Don't come to a reenactment, a historical wedding, or a Renaissance faire dressed like a 21st century American. Not only is it embarrassing to your fellow reenactors, but people will think you're not as much of a history buff as you claim. You don't need to spend tons of money on an authentic reproduction outfit, but you *can* find sewing patterns and create your own gowns, coats, trousers, etc. Whether or not you go the whole mile for historical authenticity, buying or sewing petticoats, shifts, corsets, and stockings, it's your call. You have to decide how much is too much.
(3) Check your accent when you speak. Is somebody from Cockney England going to have a Southern accent? Not likely! If possible, listen to tapes, watch TV shows, or talk to a friend with the same accent you are trying to copy. After you've spent enough time practicing, you'll realize that you know the inflections that will help you sound like a true Cockney. (Don't expect to sound exactly like them, however. Accents are extremely hard to copy perfectly unless you grew up in that part of the world. If the person you've "become" would have spoken in a voice that you simply can't duplicate, don't worry. You don't need to impress anyone; you're just having fun. Every other bit of you can be historically accurate, and no one is going to notice if you have the right accent, unless you call attention to the fact.
(4) Check out personal habits. For instance, if you're reenacting a Middle Eastern person from any era, you have to know that only one hand was used for eating. If you use the wrong hand, there's a chance no one will notice, but you won't be staying in character. If someone *does* notice, it's kudos to them, but embarrassment to you! Study the personal and cultural habits of the time period in question. There are limits, however, as in any extreme hobby. If you're portraying Attila the Hun, you don't have to pillage and plunder to stay in character, even if it was a habit of his culture! Be yourself.
(5) There are even certain rules that apply to eating. If you're visiting a medieval banquet, and everyone uses their hands to tear into that boar's leg, you don't want to be the only one with a hamburger and bottled water. Even if it's not your favorite food, you might want to grin and bear it; after all, your ancestors did, and you're trying to be just like them, right? Don't be overly obsessed with hygiene if it's not a staple of your time period; of course, a *little* hygiene is just fine and actually expected, but you don't want everyone to know you're new in the reenacting guild.
(6) Make sure you can answer a few questions about your time period. If you make it very clear that you're a 17th century Puritan, and somebody asks you what the Puritans believed, you won't look very historically accurate if you don't have a clue what to answer. This is another place where research comes in handy. You want to feel like you're a part of the culture you're trying to emulate, and finding out the basics of that culture is the first step. You don't have to be a genius and know every single little thing about your chosen era, but knowing a few basic facts always helps.