It's very rare to finish one art project with the very last drop of paint you'd put on your palette. Some supplies are easy to store for next time, such as bits of collage materials, but others, such as a little bit of paint, you may need to use straight away. Even if you haven't much time, you can put it to another creative use. What you shouldn't do is waste it by throwing it away!
Mix Up the Leftovers for Later: If it's only tiny bits of colors, scrape them up together with a palette knife and put the mix into an airtight container. A small glass jar or lidded plastic container for instance, or if you can still find one, an empty film canister. Use a knife rather than a brush because it'll get more of your palette, and because you then don't have to deal with paint stuck in the hairs of the brush!
Don't worry about what colors go in, when you mix them all together you'll end up with a greyish-brownish color. What you get depends what's in it, and while may seem rather an unappealing mixture, rather a murky mess, it's perfect for an underpainting. Use it to paint in the basic shapes using tone, or simply to get rid of the white of a canvas. As you get used to having this leftover color available, you'll find other uses for it too, such as when you're wanting an 'interesting' grey for a shadow or distant hill in a landscape for instance.
Create Small Paintings: I keep a supply of small blank canvases in my studio, no larger than the size of my hand, and have up to half a dozen I'm working on at any time. I use up leftover paint on them both at the end of the day and during a painting session. Sometimes it's wiping off excess paint from a brush while I'm working on a bigger piece or before washing it. This produces a colored ground or back background. Sometimes I scrap off all the paint on my palette using a knife and then use whatever color this mixes to eliminate the white of the canvas, spreading it around with a brush if I want less texture than using a knife will give.
On the little canvases where I've already eliminated the white, I'll start painting a scene using the individual colors still on my palette. I'll go only as far as the leftover paint lasts, then putting it aside until I've more leftovers. (It defeats the purpose to get fresh paint out of a tube!) This can lead to a many-layered painting, with all sorts colors. I try to use a bit in different places across the composition, otherwise you can end up with an irritating speck of a single color that catches the eye.
When it comes to buying small blank canvases, check with the store as you often get a discount if you buy a boxful.
Create Collage Paper: Leftover can be used to create colorful papers to use in future collage projects. Press a sheet of paper onto your palette and lift it straight up. See what you've got, and repeat or not. Or press down a sheet, then move it across a little to smear the paint. One thing's certain, the results are one-offs, unrepeatable!
More Than a Little Leftover? Then Store the Paint: Oil paint obviously doesn't dry very quickly, and is relatively easy to keep for next time. If it's only overnight, you probably don't need to do anything at all other than scrape the colors up into piles (thin paint spread across a palette dries more quickly). Acrylics can be stored too, and watercolor simply left because it can be reactivated by dampening the brush. For tips on how to do this, see:
Whatever you do, don't simply toss the paint in the bin, use it!