which way for search engines ?

I m building a multi-language website. For my website to be number 1 in search results, which way should I use about getting the language ?

1) mywebsite.com/english/posts/21

goes to post that's id is 21 and prints the post in english

the language selection was taken from the link

2)mywebsite.com/posts/21

same as before, prints the post that's id is 21

the language selection was taken from the cookie that was set by the visitor before

so for first case, google will list same post with different address

mywebsite.com/english/posts/21

mywebsite.com/french/posts/21

for second case, it s gonna be listed one time with the default language

mywebsite.com/posts/21

for the post number 21, which way is better and the link will be the number 1 in search results ?

I would pass the ISO 693-1 standard locale code into each URL, at the base though. For example:

mywebsite.com/en/posts/21

mywebsite.com/fr/posts/21

Passing it at the base would mean it's in a constant place and allow you to apply a preliminary rewrite rule before any others, meaning you wouldn't have to factor it into every other rule. Passing the locale on every page means that no search engine will be unable to differentiate between the pages, because to the best of my current knowledge GoogleBot doesn't accept cookies.

By the default language, I mean the language that was set if the user did not select any language. session[language] takes the language from the cookies.if the cookie was not set by any language, session automatically uses the default language. What I mean is I m using same structure for my other website and my pages are already indexed by google bot with the default language like mysite.com/posts/21

so does it make any difference if I change the link structure ? and do it like:

mywebsite.com/en/posts/21

mywebsite.com/fr/posts/21

In general you shouldn't be aiming to simply have different translations of your pages, but aim to have localized versions of the pages.  But even still, it will not hurt you to have separate URLs for each translation, because the search engine algorithms will not really put them in the same bucket at a higher level.  When you do a search for "apple" do you see results popping up in spanish?  Same principle.  You will have your english version page competing against other english key-word pages, and your spanish version competing against spanish keywords, etc... and Adam makes a good suggestion for how to structure your URLs for it.

But while we're on the subject of SEO...you should work on making your URLs more friendly than ".../posts/21".  I'm gonna assume that you have some sort of CMS like WordPress and those are blog/article posts... most CMSs have built-in the ability to set the URLs to be more SEO friendly than having an ID like that.  Basically they will take the title of the blog/article and use that, or some other value you specify, so that you get something more like "mysite.com/top-10-things-you-never-knew.html" or something.  This is 100x better than having an ID in the URL that means nothing to crawlers.  And if your site doesn't have something like that built-in, then you really need to invest in doing it. 

Here is a link to some SEO best-practices, straight from the horse's mouth:

http://static.googleusercontent.com/external_content/untrusted_dlcp/www.google.com/en/us/webmasters/docs/search-engine-optimization-starter-guide.pdf