I've done school admissions 7 times now, in Scotland and in England.
1st time: standard admissions for P1 (in Scotland). Super easy. I knew which school I lived in the catchment for, made an appointment during the standard window and filled in the forms with the deputy HT (who had been my P4 teacher as it was my primary school).
2nd time: in-year admission during P1. We moved to another city so DS1 needed a new school. It was simply a case of phoning schools, finding out which ones had places in P1 and choosing one. Fairly straightforward, although as with all in-year things it very much depends on where there are places.
3rd time: in-year admission moving to England. Was ok because we moved to an area where the schools mostly had places. Main problem was the utter inflexibility of the bloody system and the awfulness of the supposedly outstanding school he went to. DS1 (June birthday) went from P3 to Y3, but the school made absolutely no allowance for the fact that's he's essentially gone up a year. And the school were generally awful, but that's not the fault of the admissions system.
4th time: in-year admission for the start of Y6 because we moved to another area. This was more stressful mostly because the system refuses to allow you to apply for a place unless you're already living in the city. But you actually want to know where your child can go to school so you can make sure that you live nearby. DS1 managed to get a place in the (then) unpopular middle school in the area we moved to, but it was a very long walk from out house (past both other middle schools).
5th time: standard admissions cycle for admission to high school (Y9). Really simple. The LA has a feeder system so we were pretty much guaranteed a place (barring an absolutely huge influx of looked after children or children with statements who hadn't already had places at the feeder school with the same specialist unit - both unlikely scenarios). We'd also recently moved house and the high school his middle school feeds to is at the end of our street.
6th time: standard admissions cycle for reception for DS2 (same year as the 5th time, but it starts a couple of months later). This is more-or-less stressful depending on where you actually live because there are several 'black holes' in the local area for admission to first school. We had been aware of this when we bought our house. Where we live gives us genuinely realistic choices of first and primary schools (more than we can actually apply for), but there are several other places where there is no choice or even no guarantee of a place in a local school at all. That's just stupid.
We got our first choice (as we knew we would), but several friends ended up with their 3rd or 4th choice, which feeds to a secondary that's a long way away and bloody awkward to get to. So the feeder system is greats once you're in; not so much when getting in to first or primary school is difficult.
7th time: our (ofsted outstanding) local high school is horrible, and DS1 hated it so he wanted to go to a new free school which was doing its own admissions (it now goes through the LA system, but didn't last year). Really easy. Filled in a form online. Met with HT to talk about whether it was the school for DS1 (not an actual interview, just a chat because it's quite specialist and lots of kids would hate it). Got a Y10 place (they only take from Y10). All good and he loves it.