:(e/c) There are a couple of ways (best option (usually) first): 
 :#Provide him/her access to their talk page (if necessary).  Have them make an unblock request, laying out their case, suggesting a mentor if they have one in mind, explaining how/why things will be different, etc.  They should make it clear they're requesting and unban, not just an unblock. The admin who catches the unblock request can start a thread at WP:AN to overturn the ban. 
 :#Have the editor email WP:BASC. Note that while (I think) this is technically legit, some people believe a community ban should be overturned by the community, and it might ruffle a few feathers (not a good thing to do in an unban request).  If you think it's a reasonable request on the merits, but for some reason people dislike this person more than usual, this might be the only practical option, ruffled feathers or not. 
 :#You can start an unban discussion at WP:AN yourself. 

 :My take (just observing current mores) on current "best practice" is that this will more likely be accepted if they've sat out the ban without socking for a minumum of 3 months; preferably (but not required) have made productive contributions on another project (simple, commons, wiktionary, etc.); and are very clear on accepting responsibility for their past problems, and make very clear what they'll do different this time.