Surpanakha was an unpleasant looking sister of Ravana but in Uttar Kand it's mentioned she could change her form at will. She was widow of Vidyutjhiva, son of Kalaka. Ravana had killed him in a war and she lamented in front of Ravana who to pacify her gave her gifts and sent her away to Dandakaranya to live with Khara, their cousin.
Once when she was roaming around, she saw Shri Ram and was immediately infatuated. She approached him for love but he said he already had a wife and a woman like her wouldn't tolerate a co-wife so she should approach his brother Laxman who didn't bring his wife along. Basically he was harmlessly jesting with her thinking as a princess she would ultimately leave with dignity after rejection. She approached Laxman and he said he was just a servant and she should go back to Shri Ram.
Being a fool she couldn't understand that the Raghavas were only jesting with her and intentionally rejecting her. She thought the brothers were rejecting her due to Mata Sita who didn't say a single word to Surpanakha. She tried to attack Mata Sita to kill her but got saved by Shri Ram. Ram got angry and he said to Laxman that a sensible person must never jest with fools. He ordered him to punish her and Laxman cut her ears and nose but left her alive as she was a woman. She later said that yo Ravana they spared her life as she was a woman.
She complained to Khara who along with Dushana and Trisira took his ogres but Shri Ram single handedly defeated them. So she ran off to Lanka and complained to Ravana who at first was sceptical but when she described beauty of Sita and lied to Ravana that she went to take Sita for him , then Ravana out of his tendency of lusting every beautiful woman in the world decided to abduct her and then the tragic events happened which brought no good to anyone.