Particles are tricky, and I'm sure they must have caused problems for anyone who ever studied Japanese as a foreign language (apart maybe from Koreans, whose language I heard has similar concepts: anyone know if this is true?).
I think the main problem is that there is no equivalent concept in English. Maybe it's for this reason I find the best approach is not to assign equivalent English prepositions as much as possible.
For this reason, I think the link above might not be that useful: you end up with so many English words that could equate to the particle that it all gets too confusing.
The approach that moyashi mentions above, i.e. just remembering the function of the particle, is best, I think. If you keep these ideas in mind whilst practising as many sentences (or reading as many) as possible, things will become clearer. If you can practise in a school or with Japanese friends, then being corrected should gradually sort out mistakes.
The way of thinking which helped me was:
wa: marks the topic, used especially when introducing a new topic or contrasting
ga: marks subject/agent of the verb
ni/e: marks direction (actually a pretty direct equivalent of English "to")
ni: marks place where something EXISTS
de: marks place where an action HAPPENS
wo: marks object of the verb
The main problems that got me were, for example: when to use de and ni to mark the place, but thinking about the difference between verbs of action and the existence verbs helped, e.g.
sensei wa seitou no mae NI imasu: the teacher is in front of the students
senseu wa seitou no mae DE utatte imasu: the teacher is singing in front of the students
(my wholehearted apologies for the lameness of the example sentences)
Im sure there are a few exceptions to these general ideas, one that confused me at first is best shown in the sentence "the plane is flying through/in the sky". At first, I thought you should use "de" or "ni", but the correct one is "wo":
hikouki wa sora WO tonde imasu.
This applies to all verbs of motion (walk, run, fly etc.), where the particle "wo" is used to mark the thing that is being travelled through. But you can still think of wo as just marking the subject of the verb, meaning a direct English equivalent of this Japanese would be "the plane is flying the sky", which isn't very natural English. Still, we certainly can use phrases like "walk the street" or "sail the sea" in English. It's just that in Japanese, this type of thinking extends to all verbs of motion.
This is covered in the example sentences in the link given above in which the particle is equated to English 'through' 'in' etc. But if you consider the Japanese for "to walk in front of someone", we need wo for that, too:
hito no mae WO arukimasu
Or the phrase "walk along the street":
michi WO arukimasu
None of the English equivalents for "wo" given on this site cope with this situation, and to do so, you'd just end up adding yet another English word (for example 'along') to the list and making it more daunting and less helpful to try and remember, so again I come back to recommending the function-based approach to remembering that moyashi introduced above.
As Tom says, the difference between wa and ga is the vaguest. However, I noticed when I came to Japan. I noticed that I was using "wa" far more often than Japanese people were. Maybe it's because the first sentences we learn as beginners always use "wa", and I got into the habit of using it too much.
However, you try to remember them, the only way to get good is practising, especially via exposure to real Japanese and getting friends to correct you. I studied for 6 months in Japan, and almost every day, we had "fill in the particle" type questions, and it didn't take long to go from hating these questions to actually being pretty confident about getting them right and being able to use them correctly most of the time.
