How did Robert Baratheon become King?

Prince Rhaegar kidnapped Lyanna Stark , the one Robert loved so much. This was the spark that led to the Rebellion.

Ned's father and brother went to King's landing to ask the Mad king to stop Rhaegar but he ended up killing them both.

Robert Baratheon led a Rebellion against the Targaryens who were i control of the throne.

During the Rebellion Robert managed to defeat Rhaegar.

During the Rebellion Jaime Lannister killed the mad king by stabbing him in the back. (See Why do the Lannisters hate the Starks?)

After the Rebellion succeeded Robert was the one who had the strongest claim to the throne because his grandfather was a Targaryen.

Ned Stark and Jon Arryn didn't want to claim the Throne and so the way was Paved for Robert to become King. (See Why is Bran Stark going north of the wall?)

To the common people it was clear that the Rebellion was started by Robert and that it was his right to be the king after it was over.