Unless you dispose of the inherited property, you do not pay any capital gain tax; however, all capital gains resultiong from the disposal of inherited property are regarded as LTCGs(if the inherited property has been acquired by your father before April 1, 1981), long term capital gains.Your cost basis of the inherited property is the FMV, fair market value, on the date of death, I mean the day your father who owned it passed away. If you sell the property, then in addition to federal capital gains taxes, you'll have to pay your state CG tax on the sale of the property inheritance.if the FMV, as said above, is lower than the original cost, then the higher figure, in this case the original cost, is taken into account.
This web site is useful for further info.; http://www.irs.gov/pub/irs-pdf/p551.pdf

One clarification - if your father passed away in 2010 then your cost basis on your inherited property is equal to your father's cost basis - it is NOT "stepped up" to fair market value as of the date of death like it would have been if he passed away in 2009 or earlier.

QUOTE,"it is NOT "stepped up" to fair market value as of the date tof death like it would have been if he passed away in 2009 or earlier."--- Good point!