The new order email is sent be Magento automatically - this is default system's configuration.
First of all, check that sending emails is not disabled. Go to admin panel to the "System -> Configuration -> Sales -> Sales Emails -> Order" section. Verify there, that "Enabled" is set to "Yes".
If sending is enabled, then the application is needed to be debugged to find the actual reason. The easiest way is to setup XDebug and put a breakpoint to the start of Mage_Checkout_Model_Type_Onepage::saveOrder()
method. Then you can execute PHP step by step till you reach the $order->sendNewOrderEmail();
line. Make sure, that this line is executed. If it is not - find a reason, why, because it is a non-standard behaviour. If the line is executed, but email is not sent, the trace into this call to find the reason.
Hope, it helps.