My personal take -
Do not forget that liking something / sharing something is often visible elsewhere -- eg a public timeline, or a social widget on the blog of the user who shared / liked some of your pages.
Such would create a backlink to a specific page, which is a well known metric used by search engines (albeit not as much as it used to be). A single reference this way probably won't create any measurable effect, but if your numbers are large enough, you get the picture.
I liked this question, and could not wait to get an answer on this. So I did what any normal surfer would do ... Googled it.
This matter was widely discussed some time back with contributions from Rand Fishkin from SEOMoz, Matt Cutts from Google and the folks at Seoroundtable. Finally, the data scientist at SEOMoz published a slightly technical albeit extremely clarifying post which you need to read here.
In short - No. FB Likes do not influence SERPs.
There is correlation between higher SERPs and more likes, but correlation is not causation.
Do I need to make any other step or is enough to just put like button? Its only your own vision based on your visitors' needs. If the content stimulate users to like and share, you should do it.
Facebook likes don't influence SEO ranking. Matt Cutts said they (FB likes) can only show Google this content is interesting, but it doesn't influence ranking directly.