First of all, you've put this in the wrong forum. Questions go in the main C&C forum, this forum is only for tutorials explaining things. I'll notify a moderator to move it.
As to the question, it's very simple. Since you already know how to find the "Browse Mods" button, you're basically done. Once you've clicked the little green icon next to the mods you want, just go start a new game. (Note: you must do this through the Setup Game option within the Mods menu, NOT the New Game option back at the starting menu.) The mods, assuming they actually work, will be loaded automatically for you. There's nothing else for you to do.
Now, that assumes the mods in question actually work. Many older mods are incompatible with several of the major patches, and so just won't work any more. If you're picking mods blindly in the Mod Browser, then it's likely that at least one of the mods you downloaded is broken.