CSS is by far the easiest way to change colors. Flarum uses a lot of classes (even though I would suggest IDs in some cases), that makes customizing a breeze.
To give you a headstart: If you want to target the header on all pages, use the class header.Hero. To change it's background, you would need something like the following CSS rule:
header.Hero {
background: #f00 !important;
}
This would make your background a pure red.
The !important part after the background rule is necessary, because the color is attached to the element itself and not ruled by the CSS. Those attributions take precedence over any CSS rule unless you declare, that you want to overrule this behaviour. This is done by !important
To apply this CSS rule to the flarum homepage, you can use the Appearance section of your admin dashboard. There at the end of the section you find the possibility to customize your styles. Just copy the rule from above into the input area you see after clicking on Edit Custom CSS.
Hope this helps.