My old gaming pc did not have windows 10 and thus I couldn't use Gog galaxy. I downloaded all my games offline.

Is there an easy way to move my saved data and an installer for a game onto an external hard drive or usb so that I can then plug that in and transfer those files onto a new computer?

I am new to the whole downloading backup installers and am still learning how those work.

Unfortunately, you'll have to hunt down where each game keeps its saves. PCGamingWiki is usually a good place to find this information.
Edit: Also, if you do plan on using GOG Galaxy in the future, don't use its cloud saves feature as a substitute for your own backups. They're pretty hassle-free. The installers for larger games are split into parts, and you'll need every part to install the game. Patches can usually be ignored if you're downloading a game for the first time, because it's likely to be up-to-date already. That's about it.

Okay that is good to know about the website. So the save files wouldn't be stored in the same place as the game files?

If I downloaded games on GOG Galaxy how would I go about making a hard offline save as opposed to cloud saves?

Oh that makes sense I remember only needing one for Coromon but multiple for Fallout New Vegas

Thank you for the reply!

That might be the case for a few very old games, but generally no.
On Windows, save files typically get dumped somewhere under the AppData folder, which is hidden by default. It could be under the Roaming folder there, or Local, or LocalLow. And under there, you could have a folder named after the publisher, the developer, or the game title.
Unless the My Documents folder is used instead. There could be a folder directly under there, or under the My Games folder instead.
A handful of games instead use the Saved Games folder under your Windows user folder, like they're supposed to. This folder has existed since Windows Vista but for who knows what reason, most developers don't touch it.

And that's why you need to look up where the saves are for each game, because they could be in any number of places. I just meant you should keep regular backups of your saves, just in case. GOG Galaxy uploads saves on game exit, and downloads saves on game start (if the local save is older). But the servers might be unreachable, so you shouldn't treat cloud saves as a reliable backup. Also, there's only one copy of the saves on the server. If there's anything wrong with the local save (file is corrupt or you're in an unwinnable situation in the game), that would get uploaded to the cloud with no way back.

If you don't want cloud saves for a particular game, click the "More" button next to Play, then choose Manage Installation, then Configure. On the Features tab, you can disable cloud saves.

If you don't want cloud saves for any games, click the cogwheel in the top left, then choose Settings. In the Game Features section, you can disable cloud saves.

Gamesave Manager?

This is extremely good advice, I have long been annoyed at the black box nature of the cloud save backups on Gog. With Galaxy being finnicky with certain games, there's no way to tell if saves have even been uploaded and, if so, which ones. Hard offline backups are a must for any game where you might need to reload them.

Thank you I am going to look into all of this and hopefully I didn't delete my save folder when I deleted the Gog folder off my old hard drive to put on the new one.

That's good to know about cloud saves because honestly I am fine without those if I have hard offline saves

Thank you again!

This.