How do I extract mini lat/lon grid from bigger 277x349 lat/lon grid ?

Lets say I have a latitude and longitude variable that is Northern Hemisphere Lambert Conformal Conic grid of size 277x349 for the USA. How can I, without trial and error, pass in the southwest and northeast corners of the smaller lat/lon grid that I am trying to extract (e.g. of size 70x120, 90x140, etc. etc.). I am working with NARR data seen here: http://www.esrl.noaa.gov/psd/data/gridded/data.narr.html . I know how to guess and check and retrieve the smaller lat/lon grid that I want but this can be tedious.

Another e.g. is let's say I only want NARR data for South Dakota and not the whole USA. Once I download the whole US data how can I just extract those points which contain S. Dakota. I want the end result to be a lat/lon grid that is rectangular. I know I can use inpolygon() but that does not give me a perfect rectangular lat/lon array/grid size.

Thanks!