Please ID the grass
From the picture, it appears to be large crabgrass and some KY-31 fescue. crabgrass is an annual and can be controlled by applying a pre-emergent in the spring by April 1. KY-31 has no selective control. you would have to roundup these areas. The larger weed areas are most likely crabgrass.
Typically we reseed in the fall from late August till the end of September. I'm not sure what type of turf you have (bluegrass or lawn fescue). I prefer to use turf type lawn fescues in my lawn due to their better heat and drought tolerance and close resemblance to Ky bluegrass.
Follow these links to the UK publications that I believe will be most helpful to you. http://www2.ca.uky.edu/agcomm/pubs/agr/agr52/agr52.pdf lawn grass selection
http://www.uky.edu/Ag/ukturf/kbg.html Kentucky bluegrass varieties
http://www.uky.edu/Ag/ukturf/tf.html Lawn type tall fescue varieities