If you encounter a stain from oil paint, then act on the principle of "wedge the wedge with a wedge." Apply oil or special thinner to the stain. The range of such tools is huge. But he does not give a wholly guarantee of deliverance from spots. They can stay. Or you may just need to repeat this procedure several times.
You can deal with other types of "colorful" spots in the following way: put some well-absorbing material under the patch of fabric. It can be a sponge, gauze, cotton wool, just a cloth and cloth. Take a cotton swab or just a disc, soak it in a special solvent and apply it on the stain with blotting movements.
If the stain is old and large, then you need to leave the disc with the solvent on the fabric for several hours, you can use it all night. The solvent should destroy the stain. You just have to wash the thing.
The thermal method is sometimes used. When the paint is dissolved by heating it. The swab or solvent disc is heated with an iron and applied to stain. Be careful, because this method is not always safe, because some solvents are flammable. Read about it on the solvent packaging.
Small and very small spots are better treated with a glass or wooden stick. This method is common with expensive fabrics. And in case you need to process a large area of fabric, pull it onto a cup or other container where the solvent will drain.
The main commandment for those who struggle with paint stains: "Do not delay the removal of such stains for later." The fresher the stain, the easier it is by definition to remove it. In the first few hours, it is possible to wash them with ordinary household soap. Over time, this opportunity melts away.