Tweaking colors is one of my favorite things to do with website themes. The cool thing about having a basic background or header theme picture is the opportunity to customize the color scheme based on the actual hues in the visual (I use Gimp, a free, open-source photo editor—think Photoshop—as my tool to find colors). Works very well with my cosmology-themed sites in particular, although I have to be wary about getting carried away with too many accent colors.
Themes normally come with their own, usually very simple, color scheme, but it may not be what you are looking for. Theme makers accommodate to a lesser or larger degree in the Customize feature of WordPress sites where you can often choose your own color(s) (if you know the Hex codes for them, e.g., #243336) or one from the palette offered. Problem is, you may not know what a Hex code is or what specific one you want, and the theme may only offer you one color you can change (just the one for links and menu labels and they have to be the same, for example).
I’ll stop with the Customize option if it creates the balance of color I’m looking for (no need to fiddle too much with the site’s theme if it’s not needed), but if I want more options (special color for headings, or a text black to match my header image’s black, or a different pairing of link and hover link colors), I will use the Custom CSS feature, where you can add modified style coding from the original style sheet for the theme. This kind of customization is best done only if you know something about the tags and codes used in CSS (Cascading Style Sheets).

Quite a bit of thought and internal debate go into every color analysis; not every shade will do for every purpose (accents, hyperlinks, backgrounds, borders), and I do try to keep the three-color palette guideline in mind (as much as I love purple….). Only one color might be boring, but more than three colors, particularly accent colors, can get distracting and frankly, off-putting.
In my CW Design site here, I’ve chosen my colors based on the NGC 1097 galaxy you see in the main image. The darkest version of black becomes the text color, the paler peaches and pinks serve as backgrounds and borders for darker areas, and the more saturated pinks as borders on light/white backgrounds. The gray/blues in the image work for links and button colors, although I’ve used pink for some of the link colors with darker backgrounds. So, blue, pink/peach, and white/black form the main palette.
I’d love to know what color combos you like to work with most or see on your site. And do let me know if you’d like me to “translate” your favorite header image or logo colors into your very own color palette.