The easiest way is to start an account at Nexus skyrim and install their Nexus Mod Manager. Then just select the interesting mod and hit their "install with nmm" button.
The two I tend to rave about are the "Convenient Horses" mod and the "Ultimate Follower" mod. There's an "unofficial skyrim patch" mod that fixes a lot of small stupidities (like being unable to kill bandit/imperial camp leaders after the civil war is over) and about a dozen little mods that fix minor annoyances.
Outside of that, most of the others are 'prettifiers' (make the sky pretty, expand the weather systems, expand cities, add homes, armor, weapons, de-uglify, etc) or they substantially change gameplay (like sophisticating the sneak and lighting, altering smithing, etc.)
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