Extract the .zip file somewhere (but not in your game folder, any subfolder of your game folder, or in a folder with parentheses in the path!) (Your downloads folder is a fine choice).
Double-click install on Windows.bat¹, and follow the on-screen instructions.
Click the Log In or Register button in the upper-middle part of the Vortex main screen. A web browser should open asking whether to authorize Vortex to sync with your Nexus Mods account. That enables the Mod Manager Download buttons on Nexus mod pages. Accept the authorization.
Set up Stardew Valley in Vortex by clicking the left-hand games tab, finding Stardew Valley, and clicking it. You may wish to set up the download folder locations as well in the left-hand Settings tab.
Click the notification bell in the upper-right hand corner, which will prompt you to download and install SMAPI.
After SMAPI is installed in Vortex, click enable and you're done!
Steam: in the Steam client: right-click on Stardew Valley, choose Properties > General > Set Launch Options, and blank the launch options textbox.
GOG Galaxy: in the GOG Galaxy client: click on Stardew Valley, click the settings icon next to the 'Play' button, click Manage installation > Configure, and clear the Custom executables / arguments checkbox.
(If you want to play without mods temporarily, you can just launch Stardew Valley.exe directly or rename your Mods folder instead.)
Launch SMAPI through Steam or GOG Galaxy
If you use Steam or GOG Galaxy, and want them to track your achievements and game time, you can configure them to launch SMAPI.
If you don't care about achievements or tracking game time, you can just launch StardewModdingAPI.exe in your game folder to play with mods.
Steam
You can launch SMAPI through the Steam client to enable the overlay and achievements.
Keep SMAPI's installer window open. (If you already closed it, just run it again. No need to uninstall first.)
Copy the text in the installer window that looks like this (see how to copy text): Make sure you copy the entire line, including both quotation marks " and the %command% part. Your final path should look something like this: "Your path here" %command%
In the Steam client, right-click on Stardew Valley and choose Properties:
Click the textbox under Launch Options:
Replace anything in the textbox with the text you copied from the installer. To paste text, click in the box and press CTRL and V.
This text should consist of "Your SMAPI API Filepath" %command% Default for most users is "C:\Program Files (x86)\Steam\steamapps\common\Stardew Valley\StardewModdingAPI.exe" %command%
From now on, just launch the game through Steam to run SMAPI with the Steam overlay and achievements.
GOG Galaxy
You can use SMAPI through the GOG Galaxy client to track your play time. The steps below tell GOG Galaxy to launch a batch script, which in turn launches StardewModdingAPI.exe. This is because telling GOG Galaxy to launch StardewModdingAPI.exe directly causes the SMAPI console to be invisible, which can hide important errors and warning messages.
Open Notepad and paste in the following: start "" "C:\Program Files (x86)\GOG Galaxy\Games\Stardew Valley\StardewModdingAPI.exe" If Stardew Valley and SMAPI are not installed at C:\Program Files (x86)\GOG Galaxy\Games\Stardew Valley\, (the default location for most people), replace that location with the location of where you installed Stardew Valley.
Click on File, then Save As...
Navigate to your Stardew Valley installation folder and change the file type from Text Documents to All Files as shown below and then click Save.
Then type start.bat for the file name as shown below
In the GOG Galaxy client, click on Stardew Valle' and then the settings icon on the right-hand side of the 'Play' button, then hover over 'Manage installation' and click 'Configure...' as shown below.
A new menu will appear. Check the "Custom executables / arguments" box.
Then click 'Add another executable / arguments'
Select start.bat in the window that appears and then click Open.
Finally, click the circle next to 'Default Executable' underneath File 2, then click OK.
From now on, you can launch Stardew Valley through GOG Galaxy and both the SMAPI console and game will load as expected!
Troubleshooting
"Oops, couldn't find the game automatically"
If the installer shows that message, you can help it find the game folder. To do that: