This is a tricky question, but one I will do my best to answer in the way I feel is true. You may disagree, I hope someone does. Things would be boring if everyone thought the same way I do, and maybe there is something I can learn from you, but this is what I feel is the truth, or as close to it as I can get, after the study and research I have done.
Everything and everyone is made up of energy. This is all the same energy, just at different vibrations if you will (that seems to be a popular term for it right now). It is all the same, just in different forms, but it is all connected. The entire universe, every person, animal, object, all the empty spaces between. To simplify things, I call it either The Universe (or "U") when I am enacting my will upon it to the best of my ability, and The Powers That Be (PTB) when referring to others, or when I am frustrated that I can not make things work right.
With everything being connected and made of the same energy, we have the ability to change and alter it by changing its vibrations (there is that word again. I just don't like it, I will try to think of another that suits me better). It is all done by intent, pure and simple. Or so it should be. If we had perfect access to our minds we could simply think something, and the universe would shape itself around our whim, however there are some bumps and roadblocks in the way- mostly self imposed, and definitely for our benefit! Just imagine if every thought, every whim you ever had came instantly true. This would be horrible! Next time you got annoyed at the person who swerved in front of you in traffic, you think "That idiot is going to get himself killed!" and BOOM! Semi. Not good. So you can see how it is good that we have to really, truly work at something to make it come true. Our intent must be pure, and that is Magick.
The first roadblock to magick, to reaching out and touching the world to mold it to our liking, is the concept of Reality. Ugly, pesty thing, that. We are told all our lives what is true, what is possible, what we can and can not do... given all sorts of limitations. This means that while you are thinking "I will astral project today" your subconscious is saying "Nope, not possible, such things aren't real and even if they were you can't do it!" The best solution to this is to trick or convince your mind otherwise. This is where symbolism really comes in to play. Your brain will understand formulas, A+B=C. Now you just have to convince it that Candles+meditation=projection. Using tools lets your mind see you are taking actions, so thus a result can come of this. In a perfect world we would not need tools, it would all be done on a mental level, but the tools each have a meaning, a vibration that can act to bring you closer to your goal, and trick your mind into letting you get there. Every thing you succeed in doing will make it easier for your mind to accept that such things are real and can happen, and thus things will become easier, but tools can still be helpful to pack an extra punch. Another thing that some people disagree with but I feel worth mention, but this is where belief in G/god/s comes in handy. An almighty powerful being can do things you can't so if you "ask" it of them, your mind can set out those vibrations and allow it to happen. More on my thoughts on deities later, though.
The second roadblock is uncertainty. If you are sending out ten different messages that don't jive with each other, well, the U doesn't know what you are asking for it. Saying "I want to live in Maine and I want to travel the world and I want to be an author and I want to date beautiful women and I want to be married to the most amazing guy and have two kids and I'm a rogue adventurer" is not likely to get you anywhere, even though you feel it is all what you want. Try cutting it down to very simple terms. I want the life that will bring me the greatest joy and fulfillment, there, now you do not have to worry about asking for the wrong thing. You know you want joy, even if you don't know how you want it.
The third is being too particular. Some times something just wont work. If you put all your time and energy, focus all your intent on winning the lottery, when it is just not in the cards for you, you may miss out other things... selling an invention or manuscript, getting a new job, winning a gameshow, inheritance, who knows. Or maybe you want to get back in touch with someone, but keep telling the universe this person needs to call you, meanwhile you keep passing them in the grocery store without noticing... Once again we come down to boiling it to exactly what you want, and letting the universe put into action just how this should work. Ask for financial gain, or to see your friend again, don't say how.
Fourth is negatives. Some people say the universe does not perceive negatives; I have mixed feelings on this. I think it has a lot to do with context, but more on that later. Saying for arguments sake it is true, say you keep telling U "I have no debt". All U will see is "I have debt"-not what you want to put out there. Always try to change things to positive terms- I am financially stable. Works a mite better.
Fifth and for the moment last- others will. You are doing everything you can to make it snow. A full ritual, cast a circle, light candles, even did a little snow dance... should work, right? Well, across town someone has a flight to take, so they are doing everything the same as you for clear skies. You can see how this can get messy. Don't assume you have failed if something does not work- assume that there are other forces at work.
With all this in mind, find the style of magick that suits you best (I will of course list some here), do what you can to avoid major pitfalls, and happy casting.