For centuries, India's farmers have known that the Neem trees withstand the periodic infestations of locusts. Neem extracts applied to vegetable crops repel locusts (Heinrich Schmutterer, 1962). Like most plants, neem deploys internal chemical defences to protect itself against leaf- chewing insects. Its chemical weapons are extraordinary, however.

Neem contains several active ingredients, and they act in different ways under different circumstances.  These compounds bear no resemblance to the chemicals in today's synthetic insecticides. Chemically, they are distant relatives of steroidal compounds, which include cortisone, birth-control pills, and many valuable pharmaceuticals. Composed only of carbon, hydrogen, and oxygen, they have no atoms of chlorine, phosphorus, sulfur, or nitrogen (such as are commonly found in synthetic pesticides). Their mode of action is thus also quite different.

Neem products are unique in that (at least for most insects) they are not outright killers. Instead, they alter an insect's behavior or life processes in ways that can be extremely subtle. Eventually, however, the insect can no longer feed or breed or metamorphose, and can cause no further damage.

Add 50g of neem leaf to a pot and add 200ml of hot water and cover (justs like making a cup of tea), then after 10 minutes or so, strain and  add 500ml of room temperature water. - put in a spray bottle then apply all over your plants & insects (as long as it is cool enough).  This will last a few days before it goes off, so is suitable when you want to hit a big area.  To make a larger amount, simply multiply all the ingredients out.

This recipe is suitable to make a spray bottle up that will last ages ( so you don't have to make it up every time you garden).  Add 25ml of Neem Infused Oil to 25ml of essential oil solubuliser, shake in a bottle then add 500ml of warm water shake, then add 2lt of room temperature water. Put it in a spray bottle and spray as needed.  This will last a year or so made up.

Wa-la!

Reference for history of Neem: http://en.howtopedia.org/wiki/How_to_Use_Neem_as_a_Natural_Pesticide