Firstly, you should make sure whether the Delta Airlines will transfer your luggage to China Eastern Airlines automatically at Pudong Airport. Please contact with these two airlines companies in advance and ask them to do so if possible. On the other hand, it will save some time if you get the boarding pass from Chinese Eastern Airlines before leaving for Shanghai.

Then, when you arrive at Pudong Airport, you don't have to collect baggages. And, you don't have to go through immigration but just tell the staffs there your situation, that you have to make an international transfer at T1. Usually, they will let you pass.

At T2, you could follow the directions walking to T1, or taking the free shuttle bus to T1 in 20 minutes. Finally, please go to the international departure area and accept security inspection.