Question: As a foreigner, using articles is one of the most difficult part. 

What is the difference between "Simple is best" and "Simple is the best"? When I googled it, both appeared with many results, so it seems both are right. Are they same or have some differences?

Answer: 
Logically they are the same, but they have different psychological connotations. "Simple is best" is a bit warmer and implies that the receiver is being edified. "Simple is the best" is stated in a way that makes it sound more like it's an objective fact or something. It's kind of hard to describe.

**Edit:** After nearly ten years of considering this every time someone upvotes this, I think the difference boils down to sexuality. "Simple is best" is feminine, warm, nurturing, cunning. "Simple is the best" is masculine, cold, challenging, confrontational.
"Simple is best" is probably the phrase you want to use. 

Compare to an adage like "mother knows best." The phrase is idiomatic - a token of speech that can't be divided - so "mother knows the best" sounds wrong. 

It's harder to pin down the reason for this. In the first case, the phrase means that the simplest way is the best way. In the second case, your mother knows the best thing to do. These statements became shortened over time.

The meter of speech has a lot to do with the way idioms evolve. Words are dropped, and ungrammatical phrases may result. In this case, the idiom prescribes the grammar, not the other way around, so I don't think it's fruitful to speak of whether "best" is being used as an adjective or a noun.

Theodore Bernstein says in *The Careful Writer*: "A writer tampers with idiom at his own peril, and the peril is great. When he writes, 'At that time Sceptre was all except [two syllables] invisible in the haze,' he has flouted the idiom 'all but'."