Madara stated that he would teach Obito all of the techniques necessary to awaken the Rinnegan. At that time, Obito already had the Mangekyou Sharingan, so he could easily copy various techniques by observing them. The Sharingan doesn't just allow one to read hand seals, it also allows one to observe another's use of Chakra and match it (as Sasuke did when combining his Enton with Naruto's Rasenshuriken). Further, Spiral Zetsu noted that Obito was actually a natural when it came to adjusting to new powers after seeing how Obito quickly made use of Mokuton jutsu.
We've seen many shinobi gain power rapidly when they feel extraordinary motivation. Obito had just resolved himself to being the "Savior" of the shinobi world, and was literally living underground with nothing to do except train.
What is more, he could gain combat experience fairly safely, given that his Sharingan powers made him practically impossible for opponents to hit. Facing powerful opponents was child's play for him; only someone with Minato's speed and reaction time could hope to match his MS powers 1v1. His precognition allowed him to track even high-level taijutsu such as Guy's, as seen when Naruto, Kakashi, and Guy faced Obito in a 3v1. He could see through Genjutsu, and always either phase through the terrain or teleport away (or both). Obito even had a network of Zetsu to grant him intel, and we know that Zetsu has a vast knowledge of essentially the entirety of the shinobi world.
Kamui is much like Susano'o; it's a technique that single-handedly makes the user an S-class ninja. It's on par with the most powerful Kage-level techniques, such as Jinton or Mokuton.
