It is incredibly important to regularly clean your makeup brushes, as oils and germs can transfer easily from your face to your brush, and then every time you use them, you spread those germs around... and this can result in nasty breakouts. Also, a lot of makeup brushes are quite expensive and you'll want to protect your investment and make sure they stay in tip top condition.
Best practice is to lightly clean your brushes every couple of uses, and deep clean them once week.
Every two (sometimes three) days, I clean my most frequently used brushes (generally, just my foundation, powder and blush brushes) lightly with a makeup wipe to get rid of any left over makeup.
Once a week, I deep clean any brushes that I have used over the past seven days. I lightly dampen the brush by running it under the lukewarm water, with the brush hairs pointing down and being careful not to get any water under the handle (this can cause the glue to disintegrate resulting in hair loss - not a good thing).
Next, I squeeze a decent sized blob (see below for reference - about the size of a grape) into the palm of my hand. There are a lot of brands with dedicated brush cleaner (including Mac) but I tend to use Johnson's baby shampoo. It works just as well (I think it actually leaves the brush hairs softer) and is significantly cheaper.
I gently swirl the damp brush into the shampoo in the palm of my hand, working up a lather. My inner Monica really likes this part as you can really see the makeup washing out.
Next, I rinse the brush under lukewarm water (again, ensuring that the brush is pointing downwards to avoid getting water under the handle). It is important to ensure that all the shampoo is washed out or the residue might damage the brush hairs - if it feels slippery, keep rinsing!
The final step is to squeeze out any excess water, lightly rub the brushes back and forth on a clean, dry towel and leave them to dry overnight - I tend to roll up a towel so that the brushes are pointing slightly downwards (again, so that the water doesn't get under the handle).