The way you see the school year play out in anime - Fact (Probably kind of an easy one too guess though, secondary question: The way American's believe the Japanese school year plays out - I tend to lean a bit towards fiction.)
So this one is pretty long, but probably could be even longer, I tried and keep it bare bones and simple just laying out the structure of the school year touching upon the big events and commenting a bit on how that compares to some anime.
First lets start with the school year. The school day I'll try to have up later this week.
Japanese school, as you see in anime, starts in spring. More specifically early April so all of those classic shots of cherry blossom lined streets full of students walking to their new school ready to start the year is what it's like. Opening day varies a bit, but expect around April... 7th-ish give or take 3 days most likely. The first week is pretty much opening ceremonies, orientations, meetings and basic stuff that all students do at the start of school.
After that the next big event is Golden Week. It's a combination of 4 Japanese holidays: April 29th - Showa Day, May 3rd - Constitution Memorial Day, May 4th - Greenery Day, May 5th - Children's Day. This is your last big vacation for a long time so enjoy it. You'll have many people taking off days between to get an entire week long vacation.
Following Golden week it's pretty much regular days until summer vacation. You'll get some schools having sports festivals in this time period. June and July are crazy hot though so whenever you see shots of students sweating and complaining about the heat, it's totally justified.
Than it's summer vacation time. It will typically begin around the second to last week in July and goes until the end of August so you'll on average get about 5, probably 6 weeks of summer vacation. So yes it is much shorter then America and you get more homework and you still have club practice, but hey you get more free time then you would during school so it's nice. Obon week is the one week during summer vacation where virtually all school related stuff will shut down as students will travel with their family.
Typically summer vacation is also when the 3rd grade students will retire from their club. Some finish sooner, maybe mid July, but most stretch into late July and even August. For sport clubs it all depends on how good you do in your club's respective tournament. Get top 2, 4, 8 (varies for the given level of the tournament) in the city and move onto prefecture, then it's region and lastly national. This is also when the insanely famous and popular Koshien baseball tournament is. If you've seen a baseball anime or manga you probably know Koshien. It's just the name for High School's national tournament and it's popularity rivals professional baseball when it's happening. Some clubs do go beyond summer vacation for 3rd graders, but it's only a couple. The only ones I've personally seen are track, brass band, flower arrangement, chorus and art. The non-sports clubs usually go longer so they can do something special for the culture festival in the fall. So it's a sad and happy time for the 3rd grade students since clubs are such a big deal in Japan when you finally finish it's a major part of your school life coming to a close. It may seem early, that basically only 4 months into the school year clubs are over, but this is so they can focus on tests and getting ready for the next level of schooling.
Ok so summer vacation ended and now it's time to go back to school. During September, October, November and December the moments that stand out are culture festivals galore as well as 3rd grade students starting to prep for tests. Winter vacation starts up around the last week of December and lasts for roughly 2 weeks. On a personal note it's just crazy seeing how little of a deal Christmas is. I mean you could have school or work on Christmas and being from America that notion is kinda crazy. During winter vacation you'll have about a 4 day complete shut down period (like Obon during summer). It's typically December 30-31 to January 3-4 as many students will travel with their families during this time.
Now we are into the stretch run, January, February and March. This time is dominated by pretty much one thing, tests for 3rd grade students. In high school many 3rd grade students don't often even need to go to school anymore after their January final. You also do have Valentine's Day which I guess it's worth pointing out that girls do go kinda nuts over this and you'll have students bring in a giant bag filled with homemade chocolates to give out to friends. It's pretty much like you see with some girls trying to work up the courage to give some to a boy with the majority just giving them out to their friends. Other then that it's again business as usual for the 1st and 2nd graders. 3rd grade graduation will be about 2 or 3 weeks before the 1st and 2nd graders finish for the year and the school year will typically finish around March 24th-ish give or take 3 days. That leads us into the roughly 2 week spring vacation and back at the start.
So the idea that the Japanese school year is this long, unending, hard grind I personally find to be a bit of a myth. Yes you have just the 3 "big" vacations (spring 2 weeks, summer 6 weeks and winter 2 weeks), also they have club practice through their breaks, but and a big but, Japanese schools have wayyyyy more activities then American schools. There is always some event, activity, trip, game, special class period, anything really that's just happened, is happening, is going to happen or is being planned for. So in America, where the breaks are a lot longer and you have more free time, school days are just that school all day. In Japan it's broken up with so many different things that it can be more enjoyable, not to mention students can miss a ton of days and it's ok. So this long, unending grind of the Japanese school year while in some sense is true, I find to be a bit of a myth.