Download the Wurst Client, if you haven't already.
Extract the Wurst installer (.ZIP file) that you just downloaded.
Find "Wurst Installer.cmd" among the files you just extracted and run it.
Click the Install button.
You will normally get a message telling you that Wurst has been successfully installed.
Open the Minecraft launcher. (Close and re-open the launcher if it was already open.)
Select the new Wurst profile and press PLAY.
Download the Wurst Client, if you haven't already.
Right-click the Wurst installer (.JAR file), select "Open with" and then choose Java.
Click the Install button.
You will normally get a message telling you that Wurst has been successfully installed.
Open the Minecraft launcher. (Close and re-open the launcher if it was already open.)
Select the new Wurst profile and press PLAY.
If you see this message, here's how to fix it.
Open the Minecraft launcher, select the "Installations" tab and then press "New".
Set "VERSION" to the exact Minecraft version that you saw in the error message. Then save the profile by clicking "Create".
Launch your new installation by clicking "Play". This will start the download.
Be sure to click away any "player safety" nonsense. These warnings have nothing to do with safety!
You are now downloading Minecraft through the launcher. Once the download is complete, feel free to close Minecraft and delete your "<unnamed installation>". You won't need it anymore.
Now simply run the Wurst installer again and it should look like this.