The simple past (I read) is used when the action is finished and we focused on when the action happened ( yesterday, two days ago, last year.... or in any case we perceive it is finished.)

The present perfect ( I've read) is used when we want to emphasize the action itself ( we don't care if the action is over or not) or when the action in the past has an effect in the present. We also use it to express the duration of an action ( I have taught for 20 years... it means I am still doing it, whereas if I say I taught for 20 years it means I am no longer teaching)

Let's say:

I've lost my wallet.

So the present result is that my wallet is still lost. 

Yesterday I lost my wallet. 

We focused on the fact that YESTERDAY I lost my wallet. 

Evgeniy, I do not agree that it's a question of formality.  The English past simple* ("I read an article") and present perfect tense ("I've read an article") are used in different circumstances and convey different meanings. Knowing when to use one or the other of these tenses is a very complicated and detailed matter.  I am going to recommend these four webpages which I believe might be helpful:

http://usefulenglish.ru/grammar/the-key-to-the-present-tenses

http://usefulenglish.ru/grammar/the-key-to-the-past-tenses

*The written words "I read an article" could also be the present simple tense.  But because you are comparing it with a sentence in the present perfect, which deals with actions in the past, I assume that "I read an article" was intended to be in the past simple.

Also, be aware that the pronunciation of ‘r-e-a-d’ is different in reference to past and present tense.

Examples:

1. Yesterday I read (pronounced like the color 'red') about dogs.

2. Every once in a while I like to read (pronounced like the water plant: 'reed') a book about dogs.

You might *almost* call this a ‘homograph’, which in the strictest sense are words that are spelled same, pronounced differently, and have different meanings. With the word ‘read’, though, yes, the pronunciation changes, but the meaning is essentially the same, just not the tense.

They have the same meaning, although "I've read" is more formal.