What you will download will be a new JAR file that needs to be placed in the mods folder of the game.
There, you will find the MOD you are looking for, they all offer MODs compatible with Forge. Some of the most popular websites for this are Minecrafteo, Planet Minecraft, Minecraftmods, or Zonacraft. There are plenty of web pages of third party developers from where you can download them. Your next step is to download the MOD you want to install. Make sure that the Forge profile is available Just to the left of the Play button, you should see a new Forge profile installed, so far so good. Now, go back to the usual launcher or client. When the download and installation process is complete, you will receive a notification, click on Ok.
Select Install client and click on Ok at the bottom (make sure you have an Internet connection to download the necessary libraries). Once Java is installed, double click on the Minecraft Forge JAR file.