The following are some tips on how to revive paints that have died on you. It won't always work because sometimes, they're just too far gone.
Now the paint in the photo to the left is not too bad, but it could do with some cleaning and the following steps still apply to paints dried out even more.
The easiest method is just adding two drops of water with an eye dropper, closing up the paint, shaking it, and seeing if it's thin enough. If not, repeat.
Two drops is a safe number that shouldn't make your paint too runny.
When you have a bunch of paint gumming up the cap, the lid won't close properly, causing your paint to dry out quicker.
Whenever you notice a build up, it's a good idea to remove the excess paint. Tweezers work well.
Before it dries completely, use a toothpick to scrape it back into your paint bottle.
While you're at it, scrape under the inner rim of your bottle, forcing the clinging paint back into the bottom.
Once all the clumps are in, stir it back up. You'll probably have to add water since you're dealing with paint that's already in a water deficit.
If you're about to use the colour, you might as well use the toothpick instead of the bottle so that paint doesn't go to waste.
If you have problems with thick paint, clumps and such, drop a small ball-bearing or a small screw, nut, bolt, etc in your container. This will help mix your paint when you shake your bottle up.
Sometimes, as in the below example, the paint around the bottle has dried out too much to save. You don't want to mix this dry paint back into your bottle.
Instead, when you're scraping off the old dried or pasty paint, throw it out, rather than scrape it back into the bottle.