Again, it depends. If the MEC did NOT violate the C&BL, National will simply tell you to work within the system to affect change, all the way up to and including a recall of the LEC reps, and then the MEC Officers.
If the MEC was acting in a manner that they argue that was in the best interest of the pilot group, you may not agree with their decision, which is your right. But, if the MEC DID violate the C&BL, the National will work with you to right the wrong, especially if it's egregious.
If it's just a policy decision that you disagree with, but not in violation of ALPA's By-Laws, National will take a very hands-off approach.
All of your "how to" answers are in the ALPA Constitution and By-Laws and the ALPA Administrative Manual, which are both on the ALPA website.