Here's a pretty cool story from New Scientist: an experiment to get yeast cells to evolve multicellularity. To summarize an already short article, they bred up yeast cells, filtered them to separate any that remained single from those that formed clumps, bred up the clumpy ones, and repeated for hundreds generations. Hundreds of generations for yeast being a few weeks.
What they got was not just clumps but actual, specialized multicellular groups, in which some cells died off to improve the group's survival and reproduction odds. In other words, a previously single-celled variety of yeast had become a multicellular organism.
Now, the selection mechanism was entirely artificial, but nevertheless it seems clear that the jump from single-celled organisms to multicellular ones is not a hard step. It has apparently happened many times, among several different types of unrelated single-celled organisms. Other research indicates that it's not hard for cells to develop specialization rapidly.
Raising our eyes from the microscope to the radiotelescope, this has some interesting implications for astrobiology. Multicellularity is one of the potential bottlenecks preventing life on other worlds from developing into a technological civilization. This experiment seems to put that to rest. If you get life, it's not hard to get multicellular life.
The only question is, how easy is it to evolve intelligence? We're still trying to figure that out.