Here's a summary of the teachings about the two sets of luchos (tablets), including relevant sources.
1. The First Set of Tablets: The first set of tablets was given by God to Moses at Mount Sinai. However, when Moses descended from the mountain and saw the Israelites worshipping a golden calf, he shattered the tablets in anger. This event is described in Exodus (Shemot) 32:19:
"And it came to pass, as soon as he came nigh unto the camp, that he saw the calf and the dancing; and Moses' anger waxed hot, and he cast the tablets out of his hands, and broke them beneath the mount."
2. The Second Set of Tablets: After the sin of the golden calf, God instructed Moses to hew a new set of tablets, on which God inscribed the commandments again. This is described in Exodus (Shemot) 34:1:
"And the LORD said unto Moses: 'Hew thee two tablets of stone like unto the first; and I will write upon the tablets the words that were on the first tablets, which thou didst break.'"
3. The Placement of the Tablets: According to the Talmud (Bava Batra 14b), both the broken first tablets and the second, intact tablets were kept in the Ark of the Covenant:
"The Ark that Moses made went out to the war (against the Philistines, I Sam. IV), and in it were the Tablets of Stone that were broken."
4. Two Arks?: Rashi, a major Jewish commentator, citing this Talmudic passage in his commentary on Deuteronomy 10:1, suggests there were two Arks - one that stayed in the Temple containing the second, intact tablets, and another, made by Moses, which went into battle and contained the first, broken tablets:
"The Ark that Moses made went out to the war (against the Philistines, I Sam. IV), and in it were the Tablets of Stone that were broken."
The whereabouts of these Arks, after the destruction of the First Temple, is a matter of much speculation and mystery. They have not been seen since, and theories about their current location abound but none have been proven.