I'll start at the beginning... Spq2, what does it stand for? It's Single Player Quake 2. Easy enough, yes?
If you would like to play free Spq2 levels, it's simple. First you need to download one (or many!). You can get them right here at 3D Gamer's Edge, or go to my Links page and find some on other sites. Download the file(s) onto your hard drive.
On my computer, I've created a 'Download' folder, with a 'Quake2 Maps' folder in it, just for this purpose. Now you will need to unzip the file. You can use WinZip for this, If you have it. Just double click the downloaded level file and WinZip launches itself. If you do not have WinZip, you can get a free 21 day trial version at WinZip.com.
Here's an alternative download method that I highly recommend, as it can speed up your download times, and provide you with an in depth list of all the levels available. Head over to CDROM.com, click on the CDROM Software Archive, and look for the FTP instructions. Download the CuteFTP program that they link you to, and learn to use it.
When WinZip asks you what folder to unzip it to, click select a different folder..., and navigate to your Quake2/baseq2/maps folder. Now unzip the file. When done, go to the Quake2/baseq2/maps folder, there should be a "Read.Me" file and the map file located within. Read the Read.Me, as it will usually contain the level's story, known bugs, and other useful information.
Now write down (or memorize) the exact name of the level. Not the name of it in the Read.Me, but the name of the actual file you unzipped. It will usually be a .bsp file.
Next, just launch Quake2. When it's up and running, hit the tilde (~) key, which will bring up the console. At the console, set the skill level (easy, normal, or hard) that you would like to play at. Do this by typing "Skill 0","Skill 1", or "Skill 2". Do NOT use the quotation marks! Now hit enter. Next type in "Map mapname", no quotes! Replace 'mapname' with the name of the .bsp file. Do NOT type .bsp after the map name!
Alright! Now the level should be loading, and soon you'll be fighting with a horde of angry Strogg! Enjoy!