First of all, English is not my first language. And, very often, the usage of language and grammar will mix up with my first language.
Please help me which is the appropriate one:
Me and my friends or
My friends and I
It actually depends on context. It could be either, so here are examples of using each:
They gave gifts to me and my friends.
My friends and I went to the movies.
So, use me and my friends when something is happening to you (you are the object of the action). Use my friends and I when you are performing the action (that is, you are the subjects of the sentence).
Hope that makes sense. 
EDIT: You will often hear someone say—“Me and my friends went to the movies”, but that is bad grammar. It should be “I and my friends …”, or preferably “My friends and I …”.
[ot]
Be still, my aching heart … 
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this remark is defensible
this remark is flat out wrong
Yes, even though I said “bad grammar” above, there is a fair argument that as long as the meaning is clear, the grammar can be considered acceptable. All the same, though, there is rhyme and reason to grammatical structures, and as the language degrades, it does become less precise, which isn’t in anyone’s interest (as far as I can see). It’s somewhat analogous to sloppy HTML: though browsers can make sense of it, there’s still value in aspiring to something better.
I think I had a mini stroke too Ralph!
Being understood IS more important than grammar; but it’s said you have no hope at all of becoming reasonably proficient in a language until you understand it’s grammar more better.
Excellent analogy BTW, Ralph. Totally understandable with the perfect level of geekiousity to aid in digestion!
Thank you, ralph.m for the explanation. hm… I still do not really clear about the usage. I think I need more readings to understand more about the difference.
Since, both usages are acceptable as long as my sentence make sense, it consoles me
my main concern is that, I have to write articles sometimes to clients or some higher level personnels. English proficiency and grammar is important. It represent the company and will affect the reputation if my sentences detect a lot of grammatical error.
Feel free to post some examples of how you would use these words, and we can tell you if they are right or not.
Thank you, ralph.m for the explanation. hm… I still do not really clear about the usage. I think I need more readings to understand more about the difference.
Here’s a trick I learned for that one:
If you’re wondering if me and my friends can go to the movies… ask yourself if it’s still okay if it’s just
“me went to the movies”. Take the friends out because they are confusing the matter.
Since “me” can’t actually DO anything, you know it has to be I.
I went to the movies. Me cannot go to the movies, because stuff happens TO or FOR me.
Although I’ll warn you: there are some places where what is technically correct will sound wrong to native speakers, and they’ll think you said it wrong.
Best example I can think of right now: “I sneaked.” That is correct, but to most people, “snuck” sounds more correct. Sneaked sounds like an artificial “ed” ending on a word that sounds like it should change its inner vowels instead. Like when little kids start saying stuff like “I buyed it” or “we goed there”. (snuck is now also generally also considered correct, but it didn’t used to be)
Also, sometimes bad grammar becomes part of a “saying”. Like “Us guys gotta stick together”. Us can’t stick together, like us can’t go to the movies. WE go to the movies, and WE stick together, but “us (whatevers)” is a popular (if a bit old-fashioned) phrase.
English is an incredibly confusing language, that’s true.
I’ve heard it likened to jazz music many times.
Just like with jazz, you need to learn the rules, and then learn how to break them well.
Go for functionality first, eloquence will come. Truth be told, I see it already. Your vocabulary is great, just your grammar needs a bit of work.
By the way, you already speak better English than many of the native English speakers I know.