If somebody passed away in January of 2012?

If the decedent already filed their 2011 return you need take no further action UNLESS they have not yet cashed or deposited their refund check. In that case you will need to request the check be reissued using Form 1310 http://www.irs.gov/pub/irs-pdf/f1310.pdf

If the decedent has NOT filed their 2011 return, the spouse, executor, or other personal representative must file the return. A spouse can still file a joint return. The return must reflect that the taxpayer is deceased as the reason that the decedent is not signing the return. An executor or personal representative will need Form 1310 to have the refund check issued in their name. The person preparing the return for the decedent will sign as either surviving spouse, executor of the estate, or personal representative as appropriate.

The process needs to be repeated next year to file the decedent's final return.

yes, when the person responsible for the deceased person files the 2011 return, the date of death will be entered

also if there is a refund due, a form 1310 needs to be included

if there is any income at all in 2012, there might be a reason to file that year as well when it is time to file

Technically you have TWO final returns. Mark 2011 as deceased at top and do the same thing next year *if* they had enough income to file.

You still mark their returned as "Deceased" with the 2012 date of death as they are not exactly around to sign it or give you a pin number.