You could enforce a small time window during which the test is available. This could reduce the chance that a student who knows the answers will be free to help one who doesn't (since they both need to be taking the test at the same time).
If it's math-related, use different numbers for different students. In general, try to have different questions for different copies of the test.
If you get to design the entire course: try to have some online homeworks as well, so that you can build a profile for each student, such as a statistical analysis of how often they use certain common words and punctuations. Some students use semi-colons often; others never, for example. When they take the test you get a good idea of whether or not it's really them typing.
You could also ask a couple questions you know they don't know. For example, list 10 questions and say they must answer any 6 out of the 10. But make 3 of the questions based on materials not taught in class. If they choose 2 or 3 of these, you have good reason to be suspicious.
Finally, use an algorithm to compare for similar answers. Do a simple hash to get rid of small changes. For example, hash an answer to a list of lower-cased 3-grams (3 words in a row), alphabetize it, and then look for many collisions between different users. This may sound like an obvious technique, but as a teacher I can assure you this will catch a surprising number of cheaters.
Sadly, the real trouble is to actually enforce punishment against cheaters. At the colleges where I have taught, if a student objects to your punishment (such as flunking them on the test in question), the administration will usually give the student something back, such as a positive grade change. I guess this is because the student('s parents) have paid the university a lot of money, but it is still very frustrating as a teacher.