tl;dr: The process is terrible. Also, these notes are only relevant to the UK.
This is simplified but, in theory, the process is:
Right Move is pretty much the only option for finding houses unless you're spending over a million.
Right Move has two search options: by area/postcode or by drawing an area. For areas you can set a distance from the area which depending on where you're looking can be useful; for me, it wasn't because of various islands that are technically within a couple of miles but in reality are ~5 miles away by road. Alternatively, you can draw an area on a map and it will show you all houses within it.
You can save these searches and then enable email alerts for when new houses get added. The option says "Instantly" but it's not. In some cases, I would see a new listing and not get an email about it for 2-3 hours. The best advice is, if you can, keep the search page open sorted by recently added and periodically refresh the page.
When you call for a viewing, every estate agent wants to take your details so they can let you know about new houses. In my experience they'll just send you a few emails of stuff that's already on Right Move. They might organise a viewing for one that's in the process of being listed, but the one time this happened to me the house was nothing like what I wanted so it was a waste of time.
Stamp Duty Land Tax is a tax you have to pay when buying a house. If you're a first time buyer you pay no stamp duty if the house is worth less than some threshold, at the moment it's £500k. The government have a stamp duty calculator to work out how much you have to pay.
For solicitors, there are two choices: local firm (although in theory you could use one from anywhere) or an online one. I would recommend a local one as it makes it way easy to get in contact with them, drop paperwork off, and get things signed quickly.
Just get the meter readings as soon as you have the keys otherwise this becomes a real hassle. Everything else can wait.
Notes on Buying a House https://rknight.me/blog/notes-on-buying-a-house/
Another wiki-entry-turned-blog-post