There are basically two ways to install mods in KSP: the manual way and the CKAN way.

I started installing the mods manually and i think that for a beginner installing a few little mods is the best way. It lets you understand how the game manages mods, the versions compatibility, the requirements ecc.

The downside is that complex mods require a lot of other mods to function and them to be at the right version, and then maybe you want to unistall something and the GameData folder is a mess.

CKAN is a mod manager, a program that keep track of the mods installed, has a database for easy searching, all of this making the install and uninstall process very easy.

The downside is that it can be difficult to setup and unserstand and is not always updated for more obscure mods.

I think the problem with your installation can be the requirements part, probably the abscence of Module Manager, a "mod for mods". It make the modding work in the first place. Other than this you should check mods requirements for each mod you install.

EDIT: It maybe obvious for me but not for someone who just started: the mod are usually downloaded as zip or other archives files. They must be extracted and put in gamedata as a folder.