Getting the Entire History
Information is the key to effectively reopening your case. Everything is documented and recorded relating to removal proceedings. You will need to order the transcript of the prior hearings and file a Freedom of Information Act Request to get a copy of the government file. Also, if you had an attorney in the past represent you, request your entire file from that attorney (unless s/he continues to be your immigration attorney).
Hire a Good Attorney
There is nothing simple or easy about reopening a case when you have been removed (deported), and you only have one shot. Hire an attorney who has successfully filed many motions to reopen and will be able to write a winning motion while keeping your appeal rights in mind.
Make Sure you have "Relief"
Understand what your goal is before reopening your case. You don't necessarily want to reopen it unless you have a form of relief that you can ask the Judge to give you. If reopened, the Judge simply wants to know if you have any way of legally remaining in the United States. If you don't have a way to obtain a greencard (LPR) or some sort of other legal status in the United States, then filing a motion is or limited utility. In other words, make sure you have a way of getting your green card before reopening. This means you and you attorney need to evaluate the likelihood of success on an application for relief even before you file a Motion to quash your prior deportation.
Negotiate with the DHS and then file the Motion
If everything is lined up, have your attorney prepare a comprehensive motion with applications for relief and then negotiate with the Department of Homeland Security to determine if they will join in the motion or not oppose it. Even if they don't agree, have your attorney file the Motion to let the Immigration Judge decide to rescind your removal and reopen your case.