HEY COMMUNITY ... IM NEW TO THIS GOG SITE... JUST PURCHASED PATRICIAN 3 AND TROPICO 3... AND WONDERING HOW TO GET STARTED AFTER PUTTING THE CODES IN...

You go to your profile, you click Games and start downloading which ever video game you want to play.

If you are using GoG Galaxy then I cannot help you, because I do not use GoG Galaxy at all.

Hello and welcome to GOG.
Can you please be more specific concerning your issue? What do you mean by codes? Have you already installed the games?

I hesitate to think he got them on G2A...

If you have a code from GoG or a valid 3rd party, near the bottom of any page on the site on the left there's white text in a black bar that says 'Redeem code'

You do have the option when buying on GoG to buy directly in which case it will appear automatically in your library, or you can buy as a gift in which case they would email you the code. If you bought here, there's a history, hover over your profile picture and select 'Orders & Settings,' and that would also display the code for any games you purchased as a gift, as well as whether the game has been redeemed, and by whom.

If the games are in your library, similarly hover over your profile pic/name and select 'Games' and it will show a list of all the games you own here (excluding any you have chosen to actively hide) with various options for install.

There is a chance he bought a couple of games from Humble Bundle...

EDITED: Never mind. I just noticed the titles. Yeah, I think you're right.

Select the game, and start playing. Easy.

You account -> Games -> Click on game -> Install game

My god you people make long-winded posts that don't even answer the question. The guy already said he put the codes in.

Direct link to your library: https://www.gog.com/account

Make sure you're logged in your account while accessing the page.
And if you don't want yet another launcher getting installed in your computer, DO NOT CLICK THE BLUE BUTTON in the download options of your games. Instead, download your files from the "download offline backup game installers" section right bellow the aforementioned blue button.

Why would you tell them not to click the blue button? Rather explain what both options are. Just because you don't like Galaxy doesn't mean you should tell others who don't know not to use it. Some people may want to use it, and it seems to be GOG's preferred distribution.

To the OP, clicking the blue download and install button will install the optional Galaxy client. Many users, particularly on this forum are more old school. However, Galaxy is a mostly functional client that can be used to access your library and play your games, or back up the installers. You don't need to use it to access your library, but it is the only way to keep games automatically updated if that is your desire.

I think I made implicit with my wording what the blue button would do, and if the OP reads what's in the immediate surroundings of the blue button, it should be obvious.

Click the purple [PLAY] button.

Oh look, another of these "I HAVE A PROBLEM" topics where OP never shows up after initial post.

I was waiting for clarification.

Hmmm... couldn't have been that big a problem then.