The download page has installation instructions. This mod extends the scripting capabilities of the vanilla game, which is necessary for making many popular mods work. Next up, you'll want the newest version of the New Vegas Script Extender, or xNVSE. If desired, you can override LOOT's optimization to make manual tweaks to your load order yourself (this shouldn't be necessary for the mods in this list). This program automatically reorganizes your load order to make it as stable as possible. A great tool to pair with your mod manager is the Load Order Optimization Tool, or LOOT. This will allow New Vegas to read and accept any texture mods you install (we'll get to those later). Then go to Settings > Workarounds > BSA Redirection and toggle it. After installing it, log in, and select New Vegas as the game you're modding. I highly recommend Vortex since it has a great UI and is very easy to use.
These tools automatically handle most mods' installation, so you don't have to dig around in-game files - simply drag-and-drop compressed mod files, and the mod manager will do the rest. The first thing you need is a Nexus Mods account, the website where most mods are posted.