I have never used any site like this to buy a game, or anything for that matter. I used to play from CD ROM. Would love to play again. I've read complaints about keys and not getting stuff. I've looked, and cant find any how to. Can someone walk me thru like I am computer illiterate on how to purchase. How I will play without a CD.

Okay, well luckily on GOG there are free classics for you to get and try out.

What you get are offline installers - no need for a disc, but they do basically the same thing. What you may have heard of are dodgy Steam key resellers (Steam is a different storefront that requires a client to download the games - and theres a big grey market for the activation keys). GOG games can pretty much only be bought from GOG itself and occasionally Humble Bundle.

So... go to this link https://www.gog.com/game/beneath_a_steel_sky
Add it to your cart, then checkout (this should be obvious enough).
After, you can go to the game in your library (https://www.gog.com/account).
From there click the games icon (see attached), then "download offline backup game installers".
Click the file underneath, save it.
Once finished downloading, doubleclick the file in your downloads and it will launch an installer.
Follow the steps in the installer and enjoy!

Just like a digital videogame shop really, create account, browse for videogames, buy it with a credit card or other payment means, the game gets added to your digital library, download the game installer file, install and play game like CD's.

Gog is a fairly reputable game store, like Steam you can usually trust with your information and getting what you pay for. Unlike some less reputable means of acquiring games, dodgy sites selling cheap keys that you redeem at Gog or Steam that might not work, which are not so trustworthy giving your information too.

I thought Beneath a steel sky, Tyrian and like 3 others were already in your library by default.

THANK YOU! This is exactly what I needed and asked for! Perfect answer and simple.

Far as i know the "free library" (which i think is 13 or more games) is no longer added by default for quite some years now - this also aligns with new users having 0 games. No problem!
You can mark the thread as "Solved" by hovering over the proper post and hitting "mark as solution" on the top right of it.
Doesnt do much of anything but mark it as solved, but it is what it is.
Oh, and welcome to GOG! One more thing to note - GOG has regular sales so if you were looking at playing classic games, you may want to hold out a little. There are bigger sales every few months, weekly, weekend and special sales too.

Since the others answered your question, I'll just say welcome to GOG! This site is about the closest you can get to the golden age when you weren't forced to use game clients (though one is available if you want), back when you actually owned the games you bought instead of just leasing the rights. Even the Games page on the site is laid out like a bookshelf for your games. It's my favorite games distributor for those reasons!

Yes But you enjoy paid gaming which can give you fun more

Fun fun... Makes sense though. Some people only come for Witcher 3 and don't care about the other free games, and if i'd had that option i probably would have not gotten several of them.

First of all, welcome.

Sachys already answered brilliantly so this is basically just additional information.

What you describe here is most likely CD key shops. CD keys are like serial numbers for games. Different platforms host games -- some notable are GOG, Steam, Epic Games, UPlay (Ubisoft), Origin (EA), XBox PC Beta (Microsoft). If you buy games from these places, you buy directly from the shop that also hosts the game. They are safe.

But as you can buy the game without adding it to your account, you can also just buy the key to unlock the game for your account. It is these keys that are being sold on different CD key shops. I will not name any shops, but you can recognise them when they have games with multiple platforms. If there is say, "totallylegitgamesthataredefinitelynotascam dot com" and you see next to the games symbols for Steam, Playstation Store, Epic and such, that shop is not hosting the games, only selling the keys you would redeem on the actual platforms. And yes, there are risks. Some even use those services for money laundering. Anyone can become a seller on those platforms so there can be keys bought with stolen credit cards and such.

They only shop where I buy games from, other than directly from the shop that hosts the game, is Humble Bundle. Humble Bundle is charity and they get the keys themselves. That makes Humble Bundle a safe option, too.

GOG has also limitations for buying gift versions of games. You can buy only one copy of a game per day so those who bulk buy CD keys with stolen credit cards do not bother with GOG.

GOG is different in other ways, too. You do not need a separate launcher if you so choose. Steam, Epic Games, XBox PC and others require the launcher and live internet connection for their DRM. GOG is DRM-free and as such you can just download the installer files. They work like the CD-ROMs you are accustomed to. The difference is the files are downloaded from GOG to your hard drive and you launch the installer from there. You could burn them on CDs if you want, but I don't know many modern big titles that would fit on a CD. I have an external hard drive for the offline installers.

But I still use the GOG's own launcher, GOG Galaxy 2.0. I like it. I recommend it. Makes installing and maintaining installations easy. I also have many games from different platforms and GOG Galaxy 2.0 allows you to link all your other accounts to it so you can see everything in one launcher. You can also use it to download the offline installers or even shop for more games. But it's up to you. It is optional so you don't have to use it. I don't know any other platform that gives you this option -- or more specifically, allows you to opt-out of the launcher.

https://www.gog.com/galaxy

From all the platforms out there, the biggest ones for PC are GOG, Steam, Epic Games and XBox. GOG is the most reliable in my opinion and has no DRM. However, this no DRM policy also limits the variety slightly. Not every game publisher is ok with the no DRM policy.

Anyway, welcome again. Like Sachys said there are free games here you could try. That way you can see how everything works. Here are more free games:
https://www.gog.com/games?page=1&sort=popularity&price=free

And a lot of games are constantly on sale. Regular ones are weekend sales and midweek sales, then there are game/publisher specific sales, there are seasonal sales (summer sales, black friday sales...) so if you are looking for games on a budget, wait for sales. Build up your wishlist. Currently there's for example Fallout sales going on.
https://www.gog.com/promo/fallout_bombs_drop
Still for the next 26 hours.

There's also a giveaway thread, but you need to be an active member of these forums to qualify. What means an active member? You have to be part of a few discussions within the last month. So come to game specific topics and discuss your favourite games for a month and then you can request games that are listed here:
https://www.gog.com/forum/general/the_community_giveaway_gog_edition_redux

Also Fanatical and Amazon Prime, but so far, those two are even rarer to distribute GOG keys than Humble Bundle. @OP just a heads up: DO NOT download the installers from the big blue button right above this that Sachys mentioned.
They have the same game, but the installer comes bloated with GOG's client, GOG Galaxy, which hardly improves the experience and is a facilitator for the introduction of DRM on GOG.
If you really want a launcher for your games and you're on Windows, I suggest getting either Playnite (has similar functions and works better than Galaxy from what I could test) or WinLaunch (Android-like shortcut menu). And if you're on Linux, I saw people commenting about Lutris, I think, and you could also do some decent stuff with Alacarte if you have an in-built Android-like app menu (some distros don't, tho).

Forgot to mention, but if you're interested in deals, bundles and sales, you may want to subscribe to GOG's newsletter and check Is There Any Deal every now and then.

GOG's newsletter seems to include discount codes every Monday and Thursday now (before, it was just on Thurdays, but seems to have changed a few weeks ago), and some may be interesting for you.

And Is There Any Deal is a site that tracks prices and bundles from multiple sites, and according to the site's owner, they try to bring information about legit sites only, so no grey markets. Only bad side (if you want to sticky to a specific store), is that you need to configure filters in every page of the site when you use them (or keep the pages bookmarked, since the filters are saved on the page link and automatically loaded when you use that link).