Home-grown mesh networking

With many people now working from home every day, there's a lot more interest in improving your home WiFi coverage; and a lot of people's default answer to this question is "get a mesh network". The thing is, these things are expensive, and if you've upgraded your home network and/or WAN connection in the last 10 years (and have the bits left in a drawer somewhere) you probably actually have everything you need to build your own mesh network already.
Here's what you need to do (presented in the order that should cause minimal disruption to your home network):

Establish which router you want to be the "master"

This may be the only router currently running, the best-positioned Wifi-wise, the one with the WAN connection, all of the aforementioned, or something else.

Configure the master AP

• We'll reflect this router's status with its static IP address; ending in .1
• If you rely on a router to provide DHCP, make it this one
• Set your Wifi channel to 1,2 or 3 (for non-US locations) and do not allow it to "hop" automatically
• I'll refer to this channel as C_M
• If possible, set the Wifi transmit power to LOW

Configure your (first) slave AP

• Give it a static IP address ending in .2 (or .n for the nth device)
• Disable DHCP
• Set your Wifi channel to C_M +5 (for non-US locations) (e.g. 6 if C_M is 1) and do not allow it to "hop" automatically
• The logic behind this is to avoid overlapping frequencies
• Let's call this channel C_S
• If possible, set the Wifi transmit power to LOW
• Set your SSID, WPA scheme and password exactly as per the master

Connect master and slave via wired Ethernet

Oh and if neither of those devices is your WAN connection device, then that needs to be wired to this "backbone" too. This is super-important for good performance. If an AP can only get to the internet via Wifi, it'll be battling its own clients for every internet conversation. The Googleable name for this is "wired backhaul" or "Ethernet backhaul" and it's well worth drilling some holes and fishing some cable to get it. Don't skimp on this cable either - go for Cat6, even if your devices only (currently) go to 100Mbps.

Tune it

Grab a Wifi analyser app for your phone - IP Tools and Farproc's Wifi Analyser work well on Android. Your best option on iOS is called Speed Test - Wifi Signal Strength by Xiaoyan Huang.
Using the signal strength view, start walking from your master device towards your first slave. You should see the signal strength on channel C_M start dropping and the strength of C_S increase. Now if you've got some control over Wifi transmit strength, this is where you can "tune" the point at which your portable Wifi devices will start looking around for a "better option" - typically at around -70 to -75dBm. Remember, you actually want them to start getting "uncomfortable" quite quickly, so that they begin scanning earlier, and find the better option before you even notice any glitch. That's why we dropped our signal strength when we set the APs up - we don't want them to be too "sticky" to any given AP.

A real-life example

Prior warning - I'm a geek, so my network configuration might be a little more involved than yours, but the basics remain the same.
I have 4 devices of interest:

• WAN Modem - a TP-Link Archer v1600v that has a broken* Wifi implementation, so is just being used as a WAN Modem
• DHCP Server - a Raspberry Pi running dnsmasq - a bit more flexible than what's in most domestic routers
• Living area AP - a Linksys X6200 router/AP
• Home office AP - a D-link DIR-655 router/AP

You'll note that those APs are most definitely not state-of-the-art. When you use wired backhaul, you really don't need anything very fancy to get a strong mesh network!
Here's how they are physically laid out:

Pink lines are Gigabit Ethernet running on Cat6 cables. The red arrow is the WAN connection, which arrives at the front of the house and is terminated in the home office. That long curved pink line is the "backhaul" - it leaves the home office through a neat RJ45 panel in the skirting board, runs under the house, and surfaces through another RJ45 panel in the back of a closet in the bathroom - a little unusual, but there is power available and it is excellently positioned to cover the living area of the house as you can probably see.
Here's the configuration:

• WAN Modem - Static IP 10.240.0.1
• DHCP Server - Static IP 10.240.0.200, hands out addresses with network gateway set to 10.240.0.1
• Living area AP - Static IP 10.240.0.2, Wifi channel 3, transmit power LOW
• Home office AP - Static IP 10.240.0.3, Wifi channel 9, transmit power LOW

And that's it!
I've done a little visualisation of the signal strength using my pet project react-chromakeyed-image (more on that in another post):

You can see that the whole house is now bathed in a good strong signal, from either the living area (red) AP or the home office (green) and the only questionable area is on one side of that other front room (bottom of image), which is a playroom and doesn't need strong Wifi anyway.
(*) It actually seems to be that IPv6 advertisements can't be turned off and it advertises the "wrong" DNS addresses.