How to distinguish formal words from informal words?

I'm not sure what language you speak natively, but it's possible that your mother tongue has a more structured concept of formality that English does.

In English, formality is expressed in a number of ways. Here's a few I could think of (though there are certainly many more):

Contractions

Using contractions such as "can't" or "doesn't" is usually less formal than using their full forms (in this case "cannot" or "does not").

Word origin

Words of Latin origin are typically more formal than words of Germanic origin (for example, "assist" is more formal than "help", though they mean the same thing.

Sentence structure

Some sentences can sound more or less formal depending on where the subordinate clause is placed. For example:

"We couldn't see the mountains because of the fog."

"Because of the fog, we couldn't see the mountains."

The second, in addition to emphasizing the dependent clause more, sounds more formal.

Flourish

Sentences can sometimes be made more formal by adding words which aren't necessary to their meaning. This is common when making polite requests:

"Do you want to dance?"

"Would you be so kind as to do me the honor of dancing with me?"

The second is much more formal -- the request is "softened" by the addition of unnecessary words.

If anyone disagrees with what I've listed above, please leave a comment. One person's opinion is hardly fact.