Firstly you want to actually choose some mods and download them, the best place to find them is at http://www.justcause2mods.com/.
As an example, this tutorial will show you how to install the Increased Grapple Range & Speed mod, a great one to start off with.
1 - Go to the JustCause2Mods website, and select "Top 50 Mods" from the Mods drop down menu in the top left corner. The Increased Grapple Range & Speed mod should show up in the first few results, click on it.
2 - Now click Download at the top of the page, and it should download automatically, make sure to take note of the directory of it's downloading to.
3 - Open the zip file and leave the window open. Then, navigate to the directory where Just Cause 2 is installed (eg. C:\Program Files\Just Cause 2\).
4 - Now, right-click and create a new folder named "dropzone" without the quotes. Open your freshly created dropzone folder, and simply drag all of the contents contained in the zip file you opened earlier into this folder.
Done, now just close those windows and open up the game and test it out. This method should work for most mods you come across.
Enjoy :)
