Here's a cool study that shows evolution in action: A team of researchers including Swanne Gordon, a biology grad student at the University of California, Riverside, took guppies from the Yarra River in Trinidad and put them into a section of the nearby Damier River that is above a waterfall. Because of the barrier, this section of the river doesn't have any predators. The guppies then also colonized the part of the river below the waterfall, where they coexist with predatory fish.
How did the guppies adapt to their new environment? Rather well. After eight years and less than 30 guppy generations, the researchers discovered that the guppies above the waterfall had produced fewer and larger offspring with each reproductive cycle.
As Gordon explains:

High-predation females invest more resources into current reproduction because a high rate of mortality, driven by predators, means these females may not get another chance to reproduce. Low-predation females, on the other hand, produce larger embryos because the larger babies are more competitive in the resource-limited environments typical of low-predation sites. Moreover, low-predation females produce fewer embryos not only because they have larger embryos but also because they invest fewer resources in current reproduction.

There's also a second part to the experiment. The team took a group of guppies from part of the Yarra River that has predators and a group from a tributary that has no predators and put them in both sections of the Damier River. After four weeks, they checked back and found that the resident guppies from the first experiment—those that had already adapted to the local environment—were more likely to have survived than the newly transplanted guppies. In other words, the first set of guppies had developed a new, advantageous trait in a relatively short period of time. (Keep in mind that generations go much faster for guppies, which have a short lifespan, than for longer-lived species.)