The way it works in most places in the US is that you are assigned a school district based on your residence, and that determines which public schools children will attend. The reason for this is that local property taxes help pay for running the school, and people generally don't like paying high local taxes so that kids from another town can overcrowd their own kids' schools. That is how the free public education works.
However, assuming there is sufficient space in the school, people CAN choose to enroll their child in a different public school if they pay tuition, which basically covers the part of local taxes their kid is using so there's no added tax burden in the district where they are enrolling the kid. While a lot of people talk about this with regard to educational choice, all the times I've heard of someone actually doing this had more to do with convenience for the parents. For example, choosing a school within walking distance of their grandparents' house, who are the people watching the child after school, or keeping the kids in the school they had been attending prior to a move so they will not have to lose all their friends (this is common after a divorce when the kids are already coping with the splitting up of their parents and parents opt to not add to the stress by disrupting their school and friendships). And, yes, some people do this because they just don't like the school in their neighborhood, or decide the district boundaries don't make sense and another school really is closer to their house.
There are exceptions, as hypatia mentioned. Some school districts, in response to community pressure regarding inequality in the schools, have implemented school choice programs and magnet schools so parents can enroll their child in any school in the district and still receive that education free (if one school is much better than all the rest and everyone tries to enroll their kid there, there will be a waiting list and not every kid will really get to choose that school). In those districts, transportation is generally NOT provided to school, because kids cannot all conveniently be picked up in one location in one neighborhood and dropped off together at the same school. Of course, this doesn't fix the problem schools, it just gives some kids a chance to get out of them.
I have never known of a public school that did not have a cafeteria. School lunch programs are government subsidized to keep the cost each student pays inexpensive (or free for those below a certain income level). Some schools also offer a similar program for breakfast, having realized that kids from poor families (and many other kids who rush out too quickly without getting breakfast) are showing up to school hungry and not learning well while their stomach is growling. School-provided lunches are often quite awful (I hated them as a kid, but if you forgot your bag lunch at home, you could get an "I.O.U." to buy a lunch and bring the money in the next day, and it was better than being hungry). So, yes, these lunch programs operate at a loss by the way they are set up, because it is considered more important to make sure all the kids have food and can learn without being hindered by an empty stomach. At least, that's how it worked when I was in school. More recently, I've heard of bizarre arrangements where schools contract with places like McDonalds to provide lunches, and I have no idea how that works. It sounds apalling to me to make fast food the only option for hungry children (or to make it a condoned option at all).
Now, that's just the public schools. Parents can also choose to send their kids to private or parochial schools. Those are not subsidized by taxes, so tuition is set according to the individual schools, and the schools can choose which students they will admit. Depending on whether those schools have other sources of subsidies, and the "market value" of the education, tuition at those can range from very inexpensive (such as in the case of a not-for-profit church-subsidized school for their parishioners...the parents don't pay the full cost of the education because a lot of that comes from church donations) to extremely expensive (such as in the case of a highly competitive, private school with no subsidies, where tuition can be more than $20,000 per year). What each of those schools offer is highly variable, and one needs to take that into account as they choose a school.
As for the comment about increased spending not improving schools, that depends. One has to look at why students at a particular school are not doing well. In some cases, no, money doesn't motivate kids to show up for school, pay attention in class, do their homework, or make their parents more concerned and active in their education, and this is the problem in some failing school districts...lack of emphasis on education by their parents and peers more so than lack of available resources at the school. On the other hand, if part of the problem is that a school is still teaching from textbooks purchased in 1970 and pages are torn, missing, or students have to share books in class so can't take them home to study, money to purchase enough new textbooks for all the students would help. (Yes, in public schools, your textbooks are all provided for free, essentially on loan to you for the academic year, whereas in private schools, parents may need to buy the textbooks for their kids.) Likewise, if equipment in the classrooms is in such disrepair that it can't be used, that also can be fixed with money. If there are too few teachers in a school so that class sizes are overly large, or the school can't separate out kids into different classes for different learning speeds, then additional money to hire more teachers can help. And, of course, yes, the money has to be given and spent with a plan toward improving education and not just making the school look prettier. If kids don't have enough decent textbooks, and the school decides to spend the money they are given on new furniture for the teacher's lounge and to repaint the hallways, then that money isn't going to help when misspent. And, yes, there are schools that fail because the administrators mismanage the budget. But, there is no single answer across the board, and yes, it probably averages out that more money doesn't change anything, but only because some schools improve with more money, others don't, and others waste it on the wrong things while letting the education slip further.
Edit: And yes, Chi's scenario holds true too. If you need $10,000 to buy new textbooks for all the kids in a class and you are given only $5000, you still can't buy enough textbooks for all the kids, and nothing improves because they still are sharing books and can't take them home to study, etc. Worse, sometimes these funds come with time limits. If you haven't spent it by the end of the year, you lose it. Administrators are then faced with a choice...do they spend it to buy half the books and hope another $5000 will show up next year to buy the other half, or do they spend it on something not quite as important, but that fits within that budget? What happens if they spend the $5000 on half the books, and next year only receive $2500 toward new books, so after two years, only have 3/4 of the books they need for their students? By the third year, they get given $1000, the publisher has come out with a new, more expensive edition of the text, the old edition is no longer available, and they now have $1000 that can't be spent on any books that will help with anything, plus all the previously purchased books are sitting in storage unable to be introduced to the classroom because there aren't enough to go around yet, so the administrator spends the $1000 on maintenance instead, and gets criticized for wasting the money on something other than the books it was intended for. So, yes, there are cases when the "wasted" money is because the school isn't given everything they need when they need it, so end up using it for things further down the needs list rather than for the highest priority things on the list.
