You need the two groups of users to be identical (selected randomly) and so it is much preferred to run the groups in parallel.
For more info on how to interpret the results I highly recommend this blog: http://visualwebsiteoptimizer.com/split-testing-blog/, especially "What you really need to know about mathematics of A/B split testing" and "How large should your A/B test sample size be?" are must reads.
There is also a nice significance calculator available here.