1. Back stuff up. Your saves and .ini files in the Documents folder, as well as the mod files in your primary drive's Users/AppData/***/Local/Fallout4 folder. In the latter, plugins.txt manages enabled mods, the other two I don't really know. I suspect that DLCList.txt is used by the in-game manager to track available plugins, loadorder.txt might be what it's called.
Anyway, just back up anything you might wanna restore or have as a reference later. I even made a full copy of the install, just in case.
2. Remove any GUI mods you're using from Fallout 4/data/Interface. People using stuff like Full Dialog Interface and DEF_UI have reported crashing on startup, and it's not surprising, there are new mechanics linked to the UI in 1.5. So delete everything and reinstall after you're done, FDI has a new version which works, HUD menus I don't know. Strings for FDI I think you can leave in there, but if you want to be safe, revert to the original ones and then reinstall the modded ones later.
3. In your Documents/My games/Fallout 4 folder, if you have a Fallout4Custom.ini, open it up and remove:
[Archive]
bInvalidateOlderFiles=1
sResourceDataDirsFinal=
If you have it. Not sure if it's necessary or people reporting it are misdiagnosing problems from the Interface mods, but what the hell, do it. You should only have the default entries under [Display] in there now.
4. Now open up your Fallout4.ini and paste
bInvalidateOlderFiles=1 there instead, under [Archive] somewhere. I've seen other suggest that you instead use
sResourceDataDirsFinal to add, after STRINGS, all the other directories for MESHES, TEXTURES, etc. but this seems to work for me. If it doesn't for you when you eventually load the updated game, try
sResourceDataDirsFinal instead of
bInvalidateOlderFiles.
One more point here - if you update the game and you crash, you can try renaming Fallout4.ini and running the launcher should create a new one. If it loads with that, then go back and try changing whatever you need changed.
5. I'd suggest you start up the game to make sure you haven't removed any base asset at this point, so that if something doesn't work later, you know it's the update and not a deleted file.
6. Ok, now cross your fingers and update the game from Steam. Once done, launch it but don't click Play, just close the launcher window down again.
7. Now go and update F4SE, there's a full release for the current version of Fallout 4. Even if you haven't used F4SE,
go get it. You can launch the game with it directly, without going through either a mod manager or the default launcher.
8. Last step, edit your plugins.txt file. There's a point of dispute here, some say that the vanilla entries (Fallout4.esm, DLCRobot.esm, DLCworkshop01.esm) should no longer be featured, whereas others think that could lead to some load order conflicts. I've gone with the second camp and so far I'm not complaining. What you'll want to do is to go back to your existing plugins.txt in AppData/Local/... and an asterisk in front of each entry in the mods list. So, to give you an example:
*Fallout4.esm
*DLCRobot.esm
*DLCworkshop01.esm
*Gasmask Fix.esp
*Craftable Armor Size.esp
*Quick Save.esp
*SMC.esp
Any new mod you wanna add, just stick a new line in there, along with an asterisk followed directly by the filename of the .esp. But wait until you're confirmed to be up and running before adding anything new in the mix.
9. Ok, now you should be ready to play. Were you reaching for your mod manager? No! Bad TTLG member! Just launch via f4se.exe instead. On a serious note, I dunno, up to you, but I'm happy to leave the managers alone until the kinks are worked out.
10. Hopefully you're fine at this point and your game's in working order. If you were using Full Dialog Interface or have new mods to add, you can try them now. If you crash, try restoring the default Fallout4.ini, not sure what else to suggest as, luckily, it hasn't happened to me yet.