Others answers are really good, putting words on the method/sense I learned after years of trying and failings.
I have tried so many tools but one that helped me a lot was colors.co. Really great to practice and understand HSL (hue - saturation - lightness), which is for me the easiest way of making palettes.
Also, in most cases in web design, a good group of light colors or dark colors is one of the most important thing. So there's one things I like to do: take one primary color (main - bright) and learn to "derive" or to create shades of light colors from that main color. Ex: one bright blue and 3 light grays with a tiny bit of blue in them.