Here's how I think LoA works:
Although I don't believe thoughts can have a direct affect on your reality without some action on your part, I do believe thoughts can greatly affect what you attract in to your life, but not in the way LoA explains it.
I think most people would agree upon the fact that peoples thoughts greatly influence their actions, and so consequently what you think about will create your reality to some extent.
However, have you ever considered how much power thoughts really have over our actions? Thoughts can have a great impact on many things, for example body language, posture, facial expressions, mood, choice of clothing, manner of speech etc. So you see, if you think about it thoughts really do have a tremendous impact on our reality.
LoA puts what we attract in to our lives down to some poorly explained pseudoscientific/supernatural theory. However, I believe that the real cause for what we attract in to our lives is our actions, albeit very subtle and seemingly insignificant actions.
An example could be someone wakes up in a particularly good mood, after dreaming about a relationship with their ideal partner. Therefore, that day this person decides to spend some extra time on their hair and decides to wear their favourite bright red shirt. Lets say this person is male. His good mood is also prevalent in his posture and body language, ensuring he is sending off positive vibes to everyone that he encounters. By chance, he catches a girl smiling at him, this further increases his positive mood and now he is exuberant with confidence. At work he sees a girl who resembles the person from his dream, he decides to make eye contact with her. She smiles at him, and is attracted by his positive vibes, nice hairstyle and good dress sense. Given the positive and confident mood he's in, he decides to approach her and ask her out - unsuprisingly she accepts his invitation.
So you can see how some people might misinterpret this example and put it down to LoA, when really there is a logical explanation. The initial positive thought created a chain of actions, which ultimately led to a desirable outcome.