How does one practice suffering well?

Correct me if I'm wrong, I understand a lot of buddhism is about relieving of suffering through practicing of detachment. Removing detachment is a long process. Until one removes those attachments, there will still be suffering. My question is: until one removes all of these attachments, one will suffer. How does one deal with these sufferings? Should one try to escape these sufferings in the moment? How does one suffer "well"? And not try to escape the sufferings?