How do you do it? What is your process? Do you do it in your design tool, or with separate tools? If so, what are they?
I use Spectrum. Works quite nicely with the color picker, sampling colors out of an image, and tints/shades.
Another vote for spectrum. love that it can export css, less, sass, .ase...
There are hundreds of available online tools for making custom color palettes. Here are some: