Basically, I'm wondering how things were different from today. From the educational system and government, to hobbies and activities, anything at all. I've done a bit of research myself, but it still feels like I can't fully grasp how an average person lived their life during this time period.
You're probably going to get more meaningful answers if you're more specific about the character's sex, social class, geographic location, family circumstances, etc. "Average person" is pretty hard to pin down.
It would help if you gave us an approximate decade, too . . . for example, compulsory education was the exception at the beginning of the 19th century (although some places did have it) but much more the rule by the end of it.
For Montana frontier children, try Elliott West's Growing Up With The Country. You only mention education, hobbies, and activities. Remember that many children will have jobs.
It's very important that you narrow this search down to what decade and what location your children would be living. The difference between a child growing up in, say 1810, is a lot different from one growing up in 1890. The industrial revolution changed everything, as did the coming of the railroad, new inventions, long-distance communication, etc. The difference between city children and country children was quite striking as well. And the difference between country children living in a long-settled part of the country like the New England states would be different from a child being raised in Montana territory as well, even in the same year. Fortunately there is a LOT of information out there—including photographs—but you do have to narrow it down. Imagine if your question was: "What was life like for a child growing up in the 20th century?" You'd be spanning the horse and buggy days straight through to the internet. Lots of changes there. The changes in the 19th century were almost as startling. If you can give some notion of decade and locale, I'd be happy to point you in the direction of some information. @ChickenFreak's suggestion is excellent (I own that book myself), but only for children who grew up on the far western frontier, starting around 1850. It's not going to be much help if your children grew up in New York City in 1810. .......... If your children were growing up in the middle to later 19th century (1860s to 1880s) I can think of no better books to read than the entire series by Laura Ingalls Wilder. (Do not, I repeat, do not assume that awful TV series, Little House on the Prairie, is a substitute for reading the books.) However, her book Farmer Boy is a great account of a boy (Laura's future husband) growing up on a farm in New England in the 1860s and 70s, while the other books follow Laura and her family through settling in the west during the same period (through to the mid 1880s.) It's detailed, accurate (in terms of what conditions were like) and fun to read. You'd find a lot of your questions answered just with this series of books.
I can understand that my question was quite vague and difficult to answer. I didn't really want to involve my project in the question, and now that I read it again I can see how I might have left out some essential points. "You're probably going to get more meaningful answers if you're more specific about the character's sex, social class, geographic location, family circumstances, etc." Well, the thing is that I left those areas nonspecific because I wanted answers for all of them -- but I can see how that might have been off putting. To be more specific, I'll present a scenario: one character, a male of 15, comes from a high class family -- his father being a wealthy landowner in the US. In terms of education I'd assume that he'd have personal tutors of sorts? And if, say, his father were to die, where would all of his wealth and land go? This is just one example, there are also characters from lower class families with different circumstances. "It would help if you gave us an approximate decade..." Well, I imagine it taking place during the industrial revolution, maybe somewhere in the 1840s New York. The thing is that I created the characters before I even knew the environment, and had to tweak them the more I researched the time period. I want them to live during the 1800s industrial revolution and the implementation of railroads. Some of the characters are as young as 7, and some from 12-15. I hope that adds something of note to the question, and if you are wondering something else, just ask me.
Consider reading Philippe Aries' "Centuries of Childhood," which I actually managed to find free on the internet in pdf form! (I downloaded myself a copy, too, because why not?) The book doesn't deal specifically with the 1840's, but does talk about the general shape of childhood and how it changed from the medieval period to the modern one. This might be a useful general overview of the subject that you can use to create multiple variations on 19th century childhood. (Be aware that some of Aries' conclusions, such as that pre-modern parents didn't form deep emotional connections with their children, have been strongly challenged in the decades since the book came out.) As for your 15-year old wealthy New York boy, I suspect that he'd be sent away to school, either in the U.S. or possibly England. If his father were to die then whoever he'd named as heir would inherit. Depending on who that is, the net effect might be more or less disruptive to the life of the boy. (I have no idea what would happen if his father died intestate. You'd need someone with a background in 19th century New York probate law for that!)
