Why should I believe this stuff will work?
Most of us have at one time or another had an experience where we surprised ourselves by doing something we would not have thought we were capable of.
It may have been a physical act like throwing an "impossible" touchdown pass with a football, or an interpersonal one like delivering an impromptu speech and having every word somehow come out right.
Is this the zone?
At some point, it seems that we are no longer thinking about what we are doing, and we don't have to be. It's as if some part of us knows exactly what to do, and the 'rest' of us is just stepping aside to watch. Visualization seems to involve a similar process, allowing more capable systems to bypass the red tape of our everyday thought processes.
It gets even more intriguing: many people report getting results in the form of coincidences and ‘lucky breaks’ completely beyond the scope of their possible influence as individuals.
What is going on here?
Focus on the 'how'.
Unfortunately, far less is still known about the ‘why’s than the ‘how’s. Many religious and philosophical traditions through history have worked extensively with these ideas, but translating the metaphors is complicated. Each tradition approaches the subject differently. Interestingly, most seem to reach very similar results in the end.
Some schools of psychology speak of progressing through various levels of mastery. Westerners consider the concept of a powerful subconscious that helps us make decisions and take better advantage of situations. This fits in with the "Luck favors those who are prepared" school of thought.
More recent studies on consciousness have shown that a huge part of our thought process takes place prior to our conscious awareness of it. We are presented with results from brain research that show a decision has been made before we're even aware of the thought.
Other people have pictured a web of unseen relationships linking all things--thoughts, energies, events--that allow influence beyond the mechanical cause-and-effect that we now understand. Those with strong religious beliefs feel that the workings of God (whatever their definition) best explain for it.
What does this mean for me?
Ultimately, these questions do not need to be answered in order to take advantage of the techniques. Training your mind to help make things happen for you requires no dogma, and "faith" in its effectiveness can come simply from experiencing it being successful.