Often the best way to challenge an expert is through the use of a Daubert Motion. Below I provide some basic thoughts on how to handle the hearing.
Your initial area of challenge will be the qualifications of the expert. You should consider how many times they have been qualified as an expert in the past. However, often too great of a weight is placed on prior qualification by courts. Just because no other defense attorney has sought to challenge the "expert," does not make him an expert. Make sure that the education he has received has something to do with the subject matter about which he is going to testify. Just because someone has a Ph.D. in Chemistry does not mean he is an expert on physics. One should also inquire about the nature of his/her training - how long, who was the teacher, etc. Finally, it does not hurt to check a few publications to see the extent of his or her contribution.
The harder part is challenging the reliability and methodology of the process or method. Here are some guidelines. First and foremost, you need to learn the subject matter. As an attorney you are handicapped because you may lack the same knowledge as the "expert." Therefore, it is my practice to always learn the basics of the subject matter first. Through Daubert motions, I have challenged tire tread comparison, speed calculations based on skid marks, tool mark comparison, and statistical aspects of DNA analysis. In each case I researched and read as much as I could before confronting the witness. It helps to be able to speak the language the expert speaks.
I often focus my attack on the research that was the basis for the method. I have found that often a scientific method is based on research that was conducted 20-30 years ago using instrumentation and conditions that are simply just not appropriate today. In most cases you will find some challenge to the original research or new research which questions the old. For example, the research that is the basis for motorcycle speed calculations using skid marks is old and I think inappropriate. The motor cycles used in the research had suspensions and forks that are no longer used in today's motorcycles. You can often find more recent research questioning or challenging the original research. (Remember there are a lot of scientists and researchers trying to publish.)
Third, I always try to find the "black box" section of the method. In many cases, there is some part of the process which is very technically laden or hard to explain. Sometimes it is complicated math formula, the derivation of which escapes the expert. Other times it is a unique machine which the witnesses really does not know how it works. Regardless of its origin, finding the "black box" is important. If the expert is permitted to testify, the expert still must convince a jury. If the expert has a hard time explaining the "black box" section to you, he will rarely do it satisfactorily for a jury. Lastly, is also a good idea to employ or enlist the help on an independent expert. Often even if they are unable to conclude that the method is faulty, he will inevitably help you with tips for cross-examination.
If you are confronted with a an expert, it is important that you be represented by an experienced criminal defense attorney who is familiar with Daubert and the subject matter of the intended expert.