While cleaning paint brushes requires different materials depending on whether paint is oil- or water-based, it is generally easiest to clean brushes immediately after using them, since dried paint is significantly more difficult to remove than wet paint. It is also better to avoid soaking brushes in cleaning materials, since this can cause damage to the bristles.
For oil-based paints, cleaning solvents like mineral spirits or turpentine are effective at cleaning the bristles without causing damage. Dip the brush into a container of clean solvent several times, working the solvent between the bristles, then spin the brush on a disposable surface to remove excess cleaner. This should be repeated several times, until all of the paint is removed.
Water-based paints, like latex house paint, can be removed with warm water and mild soap. Pour warm soapy water into a clean container and work the soap into the bristles, then remove the brush and run it under clean water. This process will probably need to be repeated several times to remove all of the paint, especially if any has dried onto the brush. If soap and water are insufficient, mineral spirits or thinner can also remove latex paint, but wash brushes with warm water and soap after using these materials.