Cleaning is simple! You can either use a specially formulated product, such as MAC's Brush Cleanser or alternatively a gentle shampoo, such as baby shampoo works well. Lather up with warm water and gently work the hair of each brush from base to tip, rinsing regularly until the water runs clear. Be careful not to flood the base of the brush with water, for longevity it's best to minimise the amount of liquid that goes down into the brush shaft.
Always leave brushes to dry in natural sunlight. Resist the temptation to apply direct heat to speed up drying time as focussed heat from a hair dryer will only melt the delicate fibres & singe the hair, which ruins the brush (trust me - I've tried!) Always lay brushes flat, rather than standing them upright when drying, as this causes the water to pool at the base of the bristles, weakening the glue bonds which in turn leads to shedding.
Tools like eye lash curlers & tweezers are best wiped over with a soft antibacterial wipe & also left to dry in sunlight. While you're at it, wipe over all compacts & make-up tubes in your bag, as they too are prone to bacteria.