I have read in a book that when a person steals once, his/her right hand is cut off. If he/she steals a second time than their left leg is cut off. But what if they steal a third time? I heard that there are many opinions on this. What is done if one steals a third time? And what do the scholars say about this?
The Hanafia and the Hanbalia opinion is that if someone keeps stealing, nothing is cut off after the rights hand is cut and the left leg is cut. Rather He should be imprisoned until he repents.
It is narrated from Ali (may Allah be pleased with him) that A thief was brought to him, so he cut off his hand, and then he was brought the same thief a second time so he cut off his leg. Then He was brought a third time so Ali Said: I will not cut, if I cut his hand than with what will he eat with, and what will he wipe with? If I cut his leg than with what will he walk with? I am shy from Allah?. So he hit the man with a wood and put him in prison.
It was also narrated the same thing from Ummar (may Allah be pleased with him).
The Malikia and Shafi'iah opinion is that if someone steals a third time than his left hand is cut off, and if someone steals a fourth time, his right leg is cut off.
Abu Hurairah (may Allah be pleased with him) said: that the Prophet (May Allah's peace and blessings be upon Him) said: If a thief steals than cut off his hand, than if he steals again than cut off his leg, than if he steals again than cut his hand, than if he steals again cut his leg.
Addarqatni in his Sunan
Source: Al Fiqh Al Maliki Al Muyassar by Dr.Whbat Azzuhayli
Cutting off the hand is for the first stage of theft. For the second time, the left leg will be cut off. For the third time, the retribution is life imprisonment, and annihilation is for the fourth time. 
In prophet's time sahaba kept cutting hands and legs of the thief in alternating order until there were none left. And after 4th time (s)he committed theft, person himself/herself was killed.
Based on a hadith narrated by Jabir as in Abu Dawud Kitab Al-Hudud 20 (4410). I couldn't find the english text on the internet.