How can a scientist do a controlled experiment if it is not possible to use several different groups?

Not every experiment has control groups. If control groups are not feasible, you do what you can, and you may still learn something of interest. In the case of something like medical research, which really should have control groups, you can still use general statistical information to establish a baseline. People (for example) normally grow to a certain average height. We administer experimental drug X to our subjects, and they grow to a certain height which can be compared to the statistical average. This does tell us something.