Hello! When cleaning your makeup brushes it is important to not only remove the makeup from them, but also to get rid of the dirt, oil and bacteria. You don’t have to spend a lot of money on brush cleaner to get one that works, and I highly recommend DIY methods!
Synthetic Brushes:
+ Anti-Bacterial Dish Soap or Hand Soap
+ Baby shampoo with a bit of rubbing alcohol
Synthetic brushes are easier to clean, as the bristles won’t absorb as much product/oil/etc as natural bristles will. You don’t need to be as gentle with them, but you do need to be careful not to damage the bristles by cleaning them too vigorously. Using soap won’t dry out synthetic bristles. For really stubborn makeup that won’t come out, use a small drop of olive oil or baby oil and massage this into the bristles - don’t use too much! It’s difficult to rinse oil out of synthetic brushes.

Natural Bristles:
+ Olive oil and anti-bacterial soap
Natural bristles will dry out if you aren’t careful, and they break off easier. I use olive oil on all of my natural hair brushes to both condition the bristles and to effectively remove all of the makeup inside them.

Always remember to dry your makeup brushes upside-down; never flat or with the bristles facing upwards. Do this to keep the water from running down inside of the ferrule (metal part where the bristles meet the handle) so that you don’t loosen the glue that holds the bristles in place!
I use a clothes hanger (like this but with more clamps) to dry my brushes:

You should be washing your makeup brushes often. Dirty brushes will transfer icky things back onto your face, which can cause irritation or breakouts. It is best to wash your face brushes every day, or at least every other day; you can get away with washing eyeshadow brushes a bit less, but anything that comes very close to your eye (eyeliner brushes) should be washed more often.
If you don’t have time to wash your brushes everyday, remove excess product and sanitize them with a spot cleaner! I have a DIY video here: http://www.youtube.com/watch?v=j8lbzn49lGI&feature=g-upl
Hope this helps! :)