The Theory of Evolution says that new species can arise, and that this happened many times in the past. Some flavors of Creationism hold that new Biblical kinds cannot come into existence. There is disagreement as to the relationship of kind and species, so a new species - a speciation event - is not ruled out by many flavors of Creationism.
To talk about speciation, we first need to realize that a simple definition is inadequate. Many species alive today are stranger than you think.
From there, we can talk about the process of speciation. What would cause a speciation? What would the intermediate creatures look like? Does the parent species die? And how long would it take? The answers depend on which mechanism is involved. For example, it could be polyploidy, a genetic bottleneck, mating preference, punctuated equilibrium, or even the traditional scenario.
Fossils are often used as evidence that speciation happened in the past. But historical evidence is basically unsatisfactory. It would be nice to know if speciation has happened in the last century.