I understand that the background section says that you can tweak the existing ones to fit a campaign (PHB, p.125-126), but are there any available for making ones completely from scratch? Perhaps, say, for campaigns set in different time periods (Ancient, Classical, etc.)?
I won't reproduce the entire section here, but the key steps in the process are very similar to those laid out in the "Customizing a Background" section of the Player's Handbook/Basic Rules:
You might want to tweak some of the features of a background so it better fits your character or the campaign setting. To customize a background, you can replace one feature with any other one, choose any two skills, and choose a total of two tool proficiencies or languages from the sample backgrounds. You can either use the equipment package from your background or spend coin on gear as described in the Equipment section. (If you spend coin, you can’t also take the equipment package suggested for your class.) Finally, choose two personality traits, one ideal, one bond, and one flaw. If you can’t find a feature that matches your desired background, work with your DM to create one.
The main steps in the process listed in the "Creating a Background" section of the DMG (p. 289) are:
- Root It in Your World
- Suggest Personal Characteristics
- Assign Proficiencies or Languages
- Include Starting Equipment
- Settle on a Background Feature
Essentially, a custom background needs to have all the same things as (almost) every official background: personality traits, ideals, bonds, and flaws; 2 skill proficiencies; 2 tool or language proficiencies; some starting equipment; and a background feature.
A connection to your setting might make the background a more relevant and appealing choice for your game, but obviously being too setting-specific can make it less useful to those who would want to use it in other settings - though it might be possible in some cases to adapt the background flavor/features to work in other settings as well.
On that note, you probably should consider whether (and how well) an existing background can be reflavored or slightly modified to suit your desired background or setting before attempting to create one from scratch. For instance, there's no point making up a brand new background feature if it's essentially the same as the Folk Hero background's Rustic Hospitality feature. Even if it's not completely identical to what you want, you can still use that as a starting point, and then make slight adjustments as needed.
(The same advice applies to creating homebrew monsters, subclasses, and the like.)