recommendations for increasing the visibility and ranking of a faculty? I was wondering what it really matters for a university to climb in the university rankings, for example in Science fields such as Mathematics, Physics or Computer Science?
I found that there are the following different services to let people know about lecturer's research in a Faculty:


Google Scholar, I believe that one can put here even articles not peer-reviewed
Scopus, the service indexed by Elsevier
WebofScience, I have not used directly, but I believe is somewhat like Scopus


But I believe that services like Google Scholar are like arXiv, in the way that one can put a link to any research paper that one has made irrelevant if it was a good conference or not.

It is not better to aim to conferences that would be indexed in Scopus, DBLP, or that will use Scimago to raise the score of an institucion? 

So what is the recommendation in these cases, to try that the papers are indexed in well known sites or a new faculty should only aim to have web presence?
As ff254 correctly mentions, you are asking two different questions. "Climbing the rankings" is sort of a science of its own, and making your research be more visible to the outside is only a very minor part of it. I am not an expert on ranking optimization (I am happy to say that university rankings are not particularly relevant where I work), but if you really want to noticeably improve the ranking of your faculty, serious money and management commitment will be required (and better consulting than is available in an Internet forum).

Now, assuming that you are really more interested in making your faculty internationally more well-known. I sort of disagree with Simmy that ResearchGate is a good vehicle to achieve this goal. At least in my community, ResearchGate is not considered a "serious" source at all. Nobody goes to ResearchGate to discover new researchers (and the technical Q&amp;A forum there is a joke). People go to conferences to meet up and coming as well as established researchers. That is, if you as a new faculty want to improve your international visibility, you should:


Produce excellent research. This should be obvious, but having a bunch of mediocre papers listed in Scopus or DBLP will not make you stand out. One top paper will.
Go to as many reasonable conferences as you can. Skip on the spam ones (no interesting people will be there and publishing there will not help you in any way), but even smaller conferences usually have a lot of interesting professors in attendance. Definitely go to whatever the big conference in your field is, even if you do not have a paper to present.
Socialise. Don't be the person that just works all day in a silent corner of the conference room. Your task at the conference is not to write the next paper, but to get in touch with other researchers.
Have a nice-looking web page. Publish all your papers as preprints there. Plus points if you do  nice write-ups of your published or ongoing research in a recurring blog.
(In some communities) have a Twitter account, and follow the big wigs and engage in discussions if appropriate.