Where did the mod button on the menu go?

If there is no mods button, that means Minecraft Forge is not installed or loaded. Forge is a tool that facilitates the use of mods in Minecraft, and is a requirement for many mods.

First, make sure you are launching the game from a profile with forge selected as the version. In the launcher, check if there is a profile with "forge" in the name in the dropdown at the bottom left corner.

If not, you'll have to install Minecraft Forge. Go to files.minecraftforge.net and download the installer for the recommended version. Run it, and it will automatically create a new profile in the launcher.