Take Arun, who is preparing for a hard exam. One evening he reads about surrender and decides he has understood the Gita: "I have given it all to God. Whatever happens, happens." The next morning he does not open his books.
This is the misreading in a plain form: to surrender means to stop trying, to stop planning and to stop thinking, and to wait for what comes.
Why people read it this way
The words of the last counsel can sound like that when heard one by one. The Lord says to surrender all actions to Him (Gita 18.57), to abandon all dharmas and take refuge in Him alone, and not to grieve (Gita 18.66). Put together in a hurry, they sound like "let go of everything and let it happen". Part of this is true. A person is asked to let go of something. The question is what.
What the Lord says
The Lord has finished teaching the most secret knowledge, and he says: reflect on this fully, and then do as you wish (Gita 18.63).
विमृश्यैतदशेषेण यथेच्छसि तथा कुरु ॥ १८.६३ ॥
Thus I have declared to you knowledge more secret than the secret. Reflect on this fully, and then do as you wish.
The first thing asked is thinking. The Lord does not tell Arjuna to stop thinking. He asks him to think it through completely, and only then to choose. The choice is Arjuna's.
A few verses earlier, the Lord says that with the mind fixed on Him, Arjuna will cross all obstacles by grace. But if out of egoism he does not listen, he will perish (Gita 18.58).
अथ चेत्त्वमहङ्कारान्न श्रोष्यसि विनङ्क्ष्यसि ॥ १८.५८ ॥
With your mind fixed on Me, you will cross over all obstacles by My grace. But if, out of egoism, you do not listen, you will perish.
Read slowly, the ego in this verse is the ego that will not listen. It is not the ego of a person who makes an effort. The verse before it asks for the steady understanding along with the surrender of actions in the mind (Gita 18.57). And early in the Gita, the Lord tells Arjuna to rise and give up weakness of heart (Gita 2.3; see Arjuna's Despondency). The Gita never tells anyone to sit down.
The better reading
Surrender in the Gita hands over the worry, the claim of "I alone" and the demand over the result. The work stays, and so does the thinking. Arun does well to say, "the result is not mine to command." He goes wrong when he lets that sentence close his books.
Where to go next
The full teaching is in The Final Counsel. The ten verses are taken in order in the detailed reading. How actions are offered while the work goes on is in Offering All Actions.