Welcome to the group!
By "background" do you mean what are the criminal history requirements to OC or what is the history / process of OC in Delaware?
Open carry is de facto lawful as there is generally no law prohibiting it. There are some restrictions on where you can carry (see the FAQ link above, and for the actual laws check the Delaware Firearms Law pdf found on the FAQ page - note that a few municipalities have prohibited OC in municipal buildings since that pdf was compiled).
If you can lawfully possess guns in Delaware you can lawfully open carry them (except in the few places where carry is prohibited). The list of people prohibited from possessing deadly weapons is found here: 11 Del. C. §1448. Concealed carry requires a license, and carrying a concealed firearm without the license is a felony, so until you have the license make sure your firearm stays completely out in the open. Don't let your shirt / jacket cover it, don't stick it down in your pants, don't set it on the seat next to you then cover it with a jacket, don't stuff it way down between the seats, etc. Either on your person or accessible in a vehicle, it needs to be completely out in the open. There are several examples around the site of how people secure firearms in their vehicle while open carrying so it isn't hidden between their bodies and the car seat. Just do a search for something like "vehicle mount" for examples.
Remember that this info is only in regards to open carry in Delaware. In other states it's often completely different.