This topic is a pretty controversial one as there are many different viewpoints about it. We can all manifest anything we wish through an act of will. As you would imagine, whether we are talking about the self or Self makes a big difference about what is possible. If the wish comes from the self, then we will be attached to the outcome and, anything that is manifested, may quickly disappear. The goal is for the wish to come from the Self.
I do not think that many would argue that the Law of Attraction does not work. This law is common sense. The law essentially is that any thought that you have has its own vibration. If you expect that whatever you wish to manifest will indeed manifest and fervently declare this to be so, then that particular wish will come true. You must be specific in your request. The subtlety is to live your life as if this has already happened. A wish may be "I would like a new 2012 blue Dodge Viper" or something like that. You buy car mats for the new car of your dreams or buy drapes for that new house. In your mind, this wish has already come true.
By acting as if the object has already manifested, we change our thought forms such that we attract things into our life to make this happen. Another subtlety is that this particular thing has not manifested because we have held onto the desire too fervently. By striving after this object, we push it away. We must act without attachment, which will diminish desire. If there is no desire, our thinking is not clouded.
As you meditate that this wish has already come true, you do so regularly. You, then, wait. Be ready and the Universe will plant the seed of an idea about how to manifest this dream. This law works because it enlists the help from others, the Universe and our subconscious to make it happen. There is an incredible synergistic effect.
The controversy surrounds using spiritual practices to get material things. Some argue that this is just materialism wearing a spiritual cloak. This is where the Self comes in. If the wish comes from the Self, it is without desire. We live in an abundant Universe and there is nothing wrong with living an abundant life without lack. Act without attachment and the results are truly miraculous. This is the miracle of co-creating with the Universe.
Another teaching that arises from this is that we are all responsible for our lot in life. This is because it is our thinking that has manifested our reality. This may be a discussion for another time, but I will suggest that there is a mystery to the Universe that we cannot explain. There is karma from past lives that is working out. In short, things happen to us as part of the mystery and there is no silver bullet solution as to why things occur.
There is another part to this that covers when the manifesting is taking place that will be covered in a separate post.