How does evolution produce new species?

Evolution works in several steps. The first step is genetic modification in an individual. This can happen in a number of ways, mutation, erros in copying of the genome, radiation, or a mutated gene from a parent.

Second step is when that modification is applied in the environment. If it is beneficial, the chance of that organism surviving and producing offspring that have that gene are greater.

When species separate physically, for a number or reasons (just to use geology, let's say the continent split and the population is split with it), these beneficial (or sometimes neutral) mutations accumulate over time. After a long period, the two populations can no longer produce viable offspring, that is when we say they are different species. Speciation has occurred.

For a practical example, think of horses and donkeys, they are different species and CAN still have offspring (mules) BUT the mule is NOT viable, meaning it can`t procreate. Both horses and donkeys have a common ancestor species but their population has split some time ago and they are now different.

Hope that helps.