Can I contact the author as a reviewer?
Can I directly contact the authors to ask for clarification or I must
  conduct all correspondence via the editor? 


No, you really shouldn't contact the authors directly. I can see two options regarding the possibility of doing that: you can do it either from your normal email account (or in a similar way that discloses your identity, e.g. a phone call); or you can do it from a throwaway account that preserves your anonymity. Both of those approaches seem very wrong to me, but the first is much worse than the second.

In the first approach, you would be spoiling your anonymity as a reviewer. That would make your entire review useless. The whole point of anonymous peer review is that you can be honest in your review without having to worry about the authors knowing who you are (and without others having to worry if you were influenced by the knowledge that the authors know your identity). You may think that this is a problem only if you intend to write bad things about the paper, but it is just as much of a problem if you want to write good things, since the journal and its readers want to know that you wrote those good things out of an honest motivation and not to personally ingratiate yourself with the authors.

In the second approach, the problem of giving up your anonymity may not exist, but it's still unethical to go behind the back of the editor. The editor is responsible for the quality and the integrity of the peer review process, and needs to be informed of any communication between you and the authors. You may trust your own judgment that you would make sensible use of the information you would be getting from the authors, but the editor might disagree, and it is not your place to appropriate his or her jurisdiction over the review process. As an example, perhaps the journal or editor take the approach that the paper must be judged solely based on its submitted form with no room for clarifying questions. Or, perhaps you would reach a sensible decision to accept the paper based on additional details the authors emailed you, but you would then neglect to require them to add those details to the paper, leaving the paper flawed from the point of view of the journal and its readers - and so on; one can imagine many ways in which a reviewer, no matter how sensible and well-intentioned, can screw up this process in some subtle way due to not having the perspective and experience (and knowledge of the journal's policies) that the editor has. That is why the editor needs to be involved.


  I know that the normal
  procedure is to contact the editor, but I thought it is faster to
  directly contact the authors, as it may need multiple communications.


First of all, why should you care which way is faster? You are the reviewer. It is not your problem if the process goes slowly, it is the authors' problem, and they should have thought of including the missing details when they wrote the paper. Second of all, if multiple communications are needed for the paper to have a chance at being acceptable, then quite possibly you shouldn't be bothering to request clarification in the first place. To me this state of affairs suggests a pretty strong likelihood that the paper is simply not acceptable in its present form, so you should either flat out reject it or make a "reject and resubmit" (or "major revision required") decision, and write back with a report explaining what details need to be added or clarified to make a more in-depth evaluation of the paper possible. It would then be the authors' responsibility to comply and submit a better version if they want the paper accepted.

To summarize, it is understandable (and noble) that you want to be efficient and help the authors improve their paper. However, as a reviewer you are not required to go out of your way to help the authors with an elaborate back and forth exchange of information and critique, and you most certainly should not do so without the involvement of the editor. If you really want to have a detailed communication with the authors, I don't see anything wrong with that as long as it is done through the editor and with their approval.