No, the process is different for different phones.
There are at least two very different general install processes I have seen.
One process is used on phones on which installing a custom recovery program (TWRP or /e/ recovery) is a common and feasible practice, and where the custom recovery is then used for the process.
The other one is used on so-called A/B devices which use a different partition layout than the other phones, resulting in a different process using Fastboot Mode instead of a recovery program.
Example: Compare the instructions for Fairphone 2 (custom recovery process) and Fairphone 3 (Fastboot Mode process).
Even when using the same general process there can still be differences in detail.
For instance, it might be necessary to unlock the bootloader, or not.
Example: Compare the instructions for Fairphone 2 (custom recovery process, unlocking not needed, phone comes unlocked by design) and, I just picked that randomly, Google Nexus 4 (custom recovery process, unlocking needed).
In the end you can start with shared basics, but you’ll have to refine that into a working process for the individual device.
And then the fun starts because steps using a computer are involved, too, with subtle differences in how e.g. Windows, Linux and macOS might handle things.
The way I see it your best bets are …
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incorporating all the necessary processes and device peculiarities into the Easy Installer, so every supported device can be installed with it successfully … which is a lot of work somebody with access to respective testing devices will have to do to make it happen. Thanks to anybody adding supported devices to the Easy Installer. It helps.
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diligent community members documenting the process for a particular device/ computer OS combination with lots of explanations and screenshots. Example: [HOW-TO] Flash /e/-OS on Fairphone 3 using Debian based GNU/Linux
Thanks to anybody doing that. It helps, too. -
empowering users to be able to install manually. The less your phone and install or troubleshooting software are black boxes doing miraculous stuff, the more you own the phone and not the other way around
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Search the internet or ask in a forum how to boot your phone into Recovery Mode and into Fastboot Mode, and how to force a shutdown or reboot when the device seems stuck.
Get to know the terminal/cmd/command line. Here’s a really good and short 1 page introduction … https://tutorial.djangogirls.org/en/intro_to_command_line/ .
Get to know what ADB and Fastboot are and what they do. https://wiki.lineageos.org/adb_fastboot_guide.html is good for a short start.