An easy way to figure out which particle to use is to remember that 은/는 emphasises what comes after it, while 이/가 emphasises what comes before it. You could say that a lot of the time 는 emphasises what is being done and 가 emphasises who (or what) is doing it.

So if I my friend Jinho this question:

"진호야, 오늘 뭐 먹었어요?" (Jinho, what did you eat today?)

He might answer like this:

"나는 부대찌개를 먹었어요" (I ate Budae-jjigae) 
In this situation he would use 는 because he is emphasising what he ate, not who ate it.

But if I asked a question like this:

"야! 나의 김치가 없어졌어! 누가 먹었어?" (Hey! My kimchi has disappeared! Who ate it?)

Jinho might answer like this:

"내가 먹었어요, 미안해요." (It was me that ate it, I'm sorry). Notice how the emphasis in this sentence is the ACTOR and not the ACTION.

Don't forget that 나 becomes 내 when it comes before 가. 

This is a bit of an oversimplification and the rules about using 는/은 and 가/이 get a bit more complicated when you get into some more advanced grammar like passive/active tense and stuff but it works most of the time.  

This is a difficult to explain.  It might be easier to explain the meaning of life.  :P  Just kidding.  Lee does a great job of explaining it here: http://www.italki.com/question/117492

It is a bit easier to understand when you can see the translations of the similar sentences in which the only difference between the sentences are the use of the particles.

I am constantly using 이 or 가 when I should use 은 or 는, although I do understand when corrected.

Wow Justin! Thank you! That explains it a little better for me!

haha! No worries! I didn't notice! :-)

You are welcome.  

self correction:

This is a difficult to explain.

in which the only difference between the sentences are is the use of the particles.