In the story, a bear and tiger go to 신웅(神雄) and tell him they want to become human beings. One day 신웅 gives them a bunch of 영애(靈艾), "spiritual mugwort," and 20 cloves of garlic and tells them that if they stay out of the sunlight for 100 days and eat only the mugwort and garlic, they will become human beings. The bear and tiger take the mugwort and garlic and go into their cave.
After thirty-seven days in the cave, eating only the mugwort and garlic, the tiger gives up and leaves the cave, but the bear stays and eventually changes into a woman. The woman is called 웅녀(熊女), which means "bear woman." Apparently, there are no men around who want to marry a "bear woman," so 웅녀 frequently goes and prays under the sacred tree (神檀樹) that marks the spot where 환웅(桓雄) first came down from heaven. She prays that she will become pregnant. Hearing her prayers, 환웅 changes into human form and marries her. She gets pregnant and gives birth to a son called King Tangun (단군왕검: 檀君王儉).
I copied the Korean and Chinese below from another site. I made a few changes by trying to match up the Chinese with the different parts of the Korean translation. While doing that, I noticed that the Chinese said that the tiger left the cave after 37 days, but the translation said that it was 21 days. I just left the translation as it was in case there is some calculation I do not know about.
By the way, I wonder why the character for bear (熊) has fire (灬) under it? I have also noticed that there is fire (灬) under the character for fish (魚). Anyway, here is the story in Korean and Chinese:
이때 곰 한 마리와 호랑이 한 마리가(時有一熊一虎) 같은 굴속에 살고 있었는데 (同穴而居), 항상 신웅에게 사람이 되기를 원하였다(常祈于神雄 願化爲人) . 이때 신웅이 신령스런 쑥 한 다발과 마늘 20개를 주면서 말하기를(時神遺靈艾一炷 蒜二十校曰) "너희는 이것을 먹되 햇빛을 100일 동안 보지 않으면 사람의 형상이 되리라" 하였다 (爾輩食之 不見日光百日 便得人形). 곰과 호랑이는 그걸 얻어먹으면서 21일 동안 금기하였는데, 금기를 잘 지킨 곰은 여자의 몸으로 변하고, 호랑이는 금기를 지키지 못하여 사람이 되지 못했다 (熊虎得以食之 忌三七日 熊得女身 虎不能忌 而不得人身). 웅녀가 혼인할 상대가 없었기 때문에 매양 신단수아래에서 잉태하기를 빌자 (熊女者無與爲婚 故每於檀樹下呪願有孕), 환웅은 이에 잠깐 사람으로 변신해 그녀와 혼인하여 아들을 낳으니, 단군왕검이라 불렀다 (雄乃假化而婚之 孕生子 號曰壇君王儉).
時有一熊一虎 同穴而居 常祈于神雄 願化爲人 時神遺靈艾一炷 蒜二十校曰 爾輩食之 不見日光百日 便得人形 熊虎得以食之 忌三七日 熊得女身 虎不能忌 而不得人身 熊女者無與爲婚 故每於檀樹下呪願有孕 雄乃假化而婚之 孕生子 號曰壇君王儉