Karma phala tyaga means renouncing the fruits of action, a phrase that points to the heart of the Gita's practical teaching. It does not ask us to stop working or caring. It asks us to loosen the grip that outcomes have on our minds. The result is not indifference but steadiness: effort that continues without constant fear of losing or hunger for gaining.
Gita 18.11 says that as long as we have a body, action is inevitable, so genuine renunciation lies in giving up the fruits, and the one who does this is truly a tyagi. Gita 5.12 says peace comes from relinquishing attachment to outcomes, while craving specific results leads to bondage and anxiety, and Gita 12.12 ranks renunciation of the fruits above knowledge and meditation because peace follows it immediately. Gita 2.51 says the wise who give up the fruit are freed from the bondage of rebirth and reach the state beyond sorrow.
The Gita also suggests ways to practise. Gita 5.10 and 9.28 describe offering actions to the Divine so that they do not bind, and Gita 12.11 says that if full dedication feels out of reach, you can still act and let go of the fruits, using this attitude to reduce pressure and worry. Gita 17.17 describes discipline carried out with faith and without craving for results as pure. Do your best, then release your grip on the outcome.