Step 1: Buy and install Quake from Steam or GOG. 

Step 2: Choose and download a Quake engine source port.

• Quakespasm is probably the most popular source port. It fixes a number of bugs in the Quake engine and provides modern niceties like widescreen resolutions and support for gigs of RAM.
• vkQuake is my preferred source port becuase it works well on my low-end hardware and looks a lot like vanilla Quake, with chunky pixels and crisp textures. It's a fork of QuakeSpasm, so retains those fixes and enhancements.
• Quakespasm-Spiked takes the base QuakeSpasm source and then goes crazy on the Quake engine, removing limits and adding features while retaining the spirit of Quake aesthetics. Essential for modern Quake maps and mods like Arcane Dimensions, but overkill for anything made before the year 2000. It may be essential if you have a powerful PC because it fixes physics bugs at high framerates.
• Darkplaces adds a ton of features and graphical enhancements, but loses the vanilla look.
• nQuake or ezQuake for multiplayer. I've never used these, so I can't say much about them, but they're standard for modern Quake multiplayer gaming.

Step 3: Install your source port. Extract the source port zip file into your Quake folder. Overwrite any files if asked.

• If you bought Quake from GOG: the default install folder is C:\GOG Games\Quake
• If you bought Quake from Steam: the default install folder is C:\Program Files (x86)\Steam\steamapps\common\Quake

Step 4: Download and install a mod manager or launcher

• Everyone recommends Simple Quake Launcher 2 but I've never been able to use it reliably with oldschool maps and mods.
• I still love QuakeOn, which last had a release in 1998 but still works on modern Windows 10 systems. It's really easy to use and handles every mod I've ever thrown at it - classic or modern. Extract the qon_prog.zip file into a new directory in your Quake install: Quake\QuakeOn then run QuakeOn.exe.
  
  It will ask you to select your Quake executable, which should be the source port you installed in the previous step.
  
  Choose a mod (if needed) at top right, and choose a map from the selector at middle right.
  
  It's possible Windows may not have the right old code libraries to run QuakeOn, but it should prompt you to install and run your own automatically if required.

Step 5: Unzip your mods and maps into the right place in your Quake folder.

• If it is a map (in BSP format), extract it into the Quake\id1\maps folder.
• If it is a mod (in PAK format, possibly with other files), then create a new folder in your Quake install like Quake\MyNewMod and extract all the files in there.

Step 6: Use your Quake launcher/mod manager/front-end to select the map and mod you wish to play. Do it for Shacknews and get fragging!