According to Siddhartha, how will Gotama find enlightenment?
Isn't your question incorrectly phrased?
You're asking how will gotama find enlightenment. Gotama is the Buddha; he's already found enlightenment; that's why everyone, including Siddhartha and Govinda, flood to see and listen to him.
I suspect you meant how will Siddhartha find enlightenment. You should note that he is not gotama, and nowhere in the book does Hesse refer to him as such.
Now, if your question now becomes how will Siddhartha find enlightenment, the answer is, as the previous respondent said, "by finding your own way."
You will notice, if you read the book, that Siddhartha's finding of enlightenment echoes the way of the Buddha, yet he finds it without following the Buddha. This is Hesse's way of saying that the ways may be similar, but they still have to be individually pursued.
If you're interested in reading further, see my article at the given link.