How was Nagato able to re-awaken and control the Rinnegan?
Nagato did not need to awaken the Rinnegan. Madara already did that part for him (waiting for the Senju DNA to manifest and combine with the Uchiha DNA in order to awaken the Rinnegan). Since Nagato is an Uzumaki, which makes him a distant relative of the Senju, he can control the Rinnegan. All Nagato needed to do was activate the Rinnegan. (Senju relative + evolved Uchiha eye = Able to use Rinnegan)

The important part is Madara had the awakened Rinnegan and gave it to Nagato. Note that since Nagato received the Rinnegan and activated it, he never reverted back to normal eye form or Sharingan form. The best explanation for this is simply because Rinnegan does not cause eyestrain like the Sharingan and Byakugan. Rinnegan is the perfect eye form, and thus does not take a toll on Pain's body.

As for activation, we know that Nagato activated it upon the death of his parents. Keep in mind that these are Uchiha eyes and Uchiha has been known to have a stronger passion for love than Senju. Thus the activation of his eyes were out of love for his parents as he watched them die.

For control, the only requirements for Rinnegan is both Uchiha DNA and Senju DNA(the uzumaki clan were infact relatives of the Senju, sole holders of Sealing jutsu, to smoothen further ties and relations to the senju, and this point konoha, the 1st hokage married Uzumaki Mito, to further strengthen blood ties) which Nagato had. In general, mastering control comes with practice, just like with every other jutsu.

We know that Pain did not have full mastery of the Rinnegan as he didn't master the Outer Path. In order to use the Outer Path, Pain had to sacrifice his life when he revived everyone in Konoha.