Which planet, and how many Jedi did Luke Skywalker train when he rebuilt the Jedi Order?
He tried, but it ended poorly so he gave up.
Luke's student, Han and Leia's son Ben, turned to the Dark Side and became Kylo Ren.
As a result, Luke went into seclusion and stopped training Jedi. There seems to be some expectation that he will rebuild the Order in the future, but we'll have to wait for more films to see how that turns out.
In the old Expanded Universe, which is now the non-canon Legends continuity, Luke's Jedi Order established its home on Yavin IV, with an initial pool of 12 recruits1. From the linked Wookieepedia page:
In 11 ABY, Jedi Master Luke Skywalker chose Yavin 4 as the site for the Jedi Praxeum and the headquarters of his New Jedi Order after receiving permission from the New Republic. During his travels, he had discovered a number of Force-sensitives and finally felt ready to begin to train new Jedi. This first class consisted of twelve pupils with Luke as their teacher. Some of those twelve were Kam and Tionne Solusar, Kirana Ti, Madurrin, Kyle Katarn, Dorsk 81, Brakiss, Corran Horn, Streen, and Gantoris. Other Jedi to join soon after were Kyp Durron, Cilghal, Mara Jade, and Dal Konur.
Of course the order quickly grows beyond this, both as Luke and his Praxeum discover new Force-sensitives and as pre-Empire Jedi reveal that they were just hiding the whole time.
One example of the former, which ShemSeger points me to in comments and which is, based on your other question, possibly the incident you're referring to, occurs in issue 3 of Dark Empire II: "World of the Ancient Sith".
In this issue Luke and Kam Solusar travel to the planet Ossus, which housed a Jedi Academy millenia before the Clone Wars and was wiped out by then-Dark Lord of the Sith Exar Kun. On the planet they discover the descendants of the survivors, the Force-sensitive Ysanna. From what I can tell, only two of the Ysanna were ever trained as Jedi.
The numbers of the latter are legion, and Wookieepedia has a tremendous list of survivors of the Great Jedi Purge. Not all of them joined Luke's academy, but a good many of them did.