And now that I thought of it, here is a screen grab of the code I'm trying at the moment. I'm trying to connect to a Postgres db.

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For those who are curious, I was able to connect successfully with the changes to my code below. I changed "localserver" to "127.0.0.1". It then spat out some role error, so I went into the database and played around the roles for the db and now it seems to be good. I'll post any new discoveries here since I haven't seen many people post about this stuff on the board, and I wish there were more here about it.

OpenSQLConnection[JDBC["PostgreSQL", "127.0.0.1:5432/world_db"], 
 "Username" -> "postgres", "Password" -> "$Prompt"]

The $Prompt is great because you can just type any username and password right in there!

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Also, for some reason the "Username"/role that is entered had to match the user account I am logged into on my computer. PostgreSQL is new to me at the moment, so this might just be a n00b mistake.