Here's the main facts you need to know:
1) White light actually contains the wavelengths of every single color in the rainbow. But when our eyes receive all of those wavelengths together, it appears white to us. For example, the material of a white t-shirt reflects all the wavelengths of light back into your eyes, instead of absorbing them, making it appear white. It's also why it is suggested to wear white when it is hot out, because white clothes reflect more light rather than absorbing them (because absorbed light eventually converts to heat).
2) When white light is able to pass through a substance entirely, we perceive it as clear, potentially even invisible. For the substance to be truly invisible, the light must pass through with no refraction (where light is bent at an angle). So for example, water appears clear to use because light passes through it without being absorbed, but some light is refracted. The light later bounces off another source and will be reflected back into your eyes, so you see the color of whatever lays beyond the clear water. The refraction caused by water is what allows you to see the distortion cause by the clear liquid, rather than the liquid being truly invisible.
3) When our eyes receive only specific wavelengths of light, it appears as a specific color to us according to which wavelength our eye is sensing. For example, if a t-shirt appears green to us, it is because the pigment in the t-shirt is absorbing all of the wavelength of light EXCEPT for the green wavelength. The green t-shirt is actually reflecting green light back into our eyes, which is why it appears green. That means the pigment in the green t-shirt is actually absorbing red, orange, yellow, blue and purple wavelengths of light.
4) When our eyes receive no (or neglgible) specific wavelengths of light, it appears to use as black.
I'll need to use two examples here, because black is a nifty, weird case.
a) There is NO true black pigment!!! Black ink is not actually black, it is a combination of ink pigments. If you use chromatography to separate black ink, you will discover that black ink is actually a mixture of dark blue, purple, and green ink, sometimes even reds and yellows depending on the "recipe". So a black t-shirt actually absorbs (nearly) all the visible colored wavelengths of light and our eyes interpret that as the dark blackness. It's why black-colored items heat up more in the sun that white, because they are absorbing more light, which becomes heat!
b) True black, true darkness is the absolute absence of light. Most humans have never seen true darkness, due to light pollution. There are a few beautiful, secluded national parks where you can experience this on a moon-less cloudy night. My suggestion would be to go on a cave tour, where they ask everyone to turn off all of their flashlights. It is a very disorienting feeling to have no light around you.
What a great question! Thanks for asking.