the Jedi (used to) have a Jedi Council, do the Sith also have similar organization? If so, who's the grand master/leader/president?
The Sith Order followed the Rule of Two for almost the entirety of its documented history in canon. Under the Rule of Two, the leader of the Sith is the Sith Master. The Sith Master commands only a single Sith apprentice since the Rule of Two requires only two active Sith at one time. The Sith Masters named in canon are
Darth Bane was the Sith Lord who introduced the Rule of Two, and he lived about a millennium before the events of the films. Before he instituted the Rule of Two there were many Sith Lords, but the structure of the Sith Order at that time is not explained in canon. The Rule of Two was introduced by Darth Bane to prevent infighting amongst the Sith, so the Sith hierarchy before the Rule of Two was apparently not stable.
Darth Plagueis was Darth Sidious' master, and Darth Sidious is more commonly known as Emperor Palpatine.
The Sith Order appears to be extinct as of the deaths of Darth Sidious and his final apprentice, Darth Vader, at the end of Episode VI. There are dark side users in Episode VII named Supreme Leader Snoke and Kylo Ren; however, Kylo Ren is not a Sith (and presumably neither are the other Knights of Ren) and it is not known whether Supreme Leader Snoke is a Sith.