There are very rational explanations on where and how to use particles. 

は and　が do NOT function in the same way. There are only a few circumstances in which they can be swapped such as when you are comparing and constrasting information.

Wa has several usages but its basic function is to set off a topic. 

Ga indicates the subject of the sentence or with certain verbs or adjectives, the object. 

1. Ga can idicate existence when used with the verbs aru, gozaimasu, iru, and irassharu 

2. Ga can idicate the subject of the predicate.

3. When you are presenting new unknown information.  

No is a particle used to indicate posession. Watashi no hon= My book. 

を is a particle used when you are performing an action. Ex. I'm eating cookies, I bought a book, etc However, if you want to say you went somewhere (aka performing an action of travel) you have to use the particle に。Ni is also used to indicate where something is located. Ex. "She is in that building". 

A more complete explanation would take up too much space LOL. But there are plenty of resources that you can use to help you. I really like the book "All About Particles" By Naoko Chino

Detailed descriptions of 「は」、「が」 and 「の」 particles can be found in Tae Kim's guide: http://www.guidetojapanese.org/learn/grammar/particlesintro for 「は」 and 「が」, and http://www.guidetojapanese.org/learn/grammar/nounparticles for several noun-reated particles, 「の」 included. Here's a brief description of what they do:

As the name suggests, topic marker sets or changes the sentence's topic (not the subject, mind you). Identifier comes in handy when you need to point out one thing among several candidates or when you don't know the topic, like in questions. And it has nothing to do with the subject, either. In fact, there's no way to specify subject in Japanese language: it depends purely on the context. There's only one strict rule regarding topic and identifier particles' usage: topic marker can't be used with question words.
The 「の」 particle has a lot of uses. When attached to a noun, it allows it to modify another noun. It doesn't necessarily indicate possession, as explained on the page I gave you a link to. Also, it can serve as a generic noun, allowing to treat verbs and adjectives like nouns (marking them as topics or direct objects, for example). When placed the end of the sentence, the 「の」 particle makes it sound like an explaination.

Phew... That wasn't really brief, now was it? Anyway, the best way to develop an understanding of particles is by practicing. And check the links I gave you. The information there is sure to help you with your question. Trust me on that.