Picking "random" numbers
Often in a report of a randomized clinical trial, you see description in the methods section of the paper indicating a bit more detail than just saying "patients were randomly assigned to treatment or control." Due to recognized (and unrecognized), internal (and possibly external) potential sources of bias, it's virtually impossible for a human to truly randomly pick numbers.
Dave of Cognitive Daily conducted an experiment earlier this month that illustrates this point very well -- he asked readers of his blog to pick any number between 1 and 20, and tabulated the responses. He reports the results in this post. Charting 347 responses from humans against 347 random picks made by a computer, it is clear that the distribution of the human selections are not randomly distributed -- humans were much more likely to select the number 17, far beyond what would be expected if the distribution was truly random.
(he also sums up reader comments on the experiment in this post and makes some inferences about why the number selection wasn't random)
So if we can't pick numbers randomly, how do researchers get random numbers for use in projects like randomized controlled trials?
There are a number of sources, including computer-based random number generators (e.g. the True Random Number Service, Microsoft Excel's random number generator) or a table of random numbers (e.g. the table on this page from the Partnership for Kentucky Schools -- the instructions provide a walk-through example for those who are interested in doing a little exercise about how you really use these numbers to randomly assign people to groups).
Researchers use these kinds of tools to randomize patients, and typically provide some explanation of their process for randomization in the Methods section, as noted above (e.g. the randomization section of the methodology in this article by Taha et al. in PLoS Clinical Trials).