How was the Election of 1876 "stolen?"
To say that this election was "stolen" is to make a judgement as to who should have won. It is not clear who was legally the more deserving winner in this election. There are cases to be made for both sides. The way the election was decided was purely political.
In the South at this time, there was conflict between the Democrats who wanted an end to Reconstruction and Republicans who typically wanted it to continue. In a few states, different slates of electors were certified by one government official or another after the election. For example, Florida's Republican governor signed for a slate of Republicans while its Democratic Attorney General signed for another. It was very hard to know whose claim was legally more solid.
What ended up happening is that an Electoral Commission was set up to decide who would be president. Eventually a compromise was reached where Hayes was elected president and Reconstruction was ended.
We have no way of saying objectively that the election was stolen. Instead, we can say that it was decided in extremely unusual circumstances, but both sides agreed to the result.