We learn about the escape in Ch. 20. It took quite a bit of preparation, including steps that they plan to take both before and after Jonas leaves the community. Here are the first three steps to get you started.
One of the first steps is that Jonas and the Giver plan to delay the escape for a couple of weeks so they had time for the Giver to
"transfer memory of courage and strength that he could to Jonas. He would need those to help him find the Elsewhere that they were both sure existed. They knew it would be a very difficult journey" (Ch.20).
Next, they decide Jonas will need to leave his house the night before the December Ceremony. This is very dangerous, though, as no member of the community is allowed out of their house at night unless they are on "official business," which of course he would not be.
Then, Jonas would sneak over to the Giver's Annex, where they plan to sneak him out in a car the next morning. The Giver plans to call for a car to take him to another community and then send the driver away for a few minutes to get something and while he is gone, Jonas would sneak into the trunk of the car and hide with food the Giver had been storing from his own meals.
It is important to remember none of this takes placed as planned because Jonas's father changes everything by saying that Gabriel is schedule for release the next morning. Therefore, Jonas decides on his own, that night, to leave with Gabe in the middle of the night.