Crab grass will die at the first hard frost, as stated above. The best way to defeat it is with a good pre-emergent appled when the forsythia bloom, as RUrichdog said. Prodiamine (Barricade) lasts the longest. PEndimethalin is in some Scotts products and is good too. I like Dithiopyr (Dimmension) the best since it has both a pre and post emergent impact. The duration of these is generally 3-6 months depending on rate and other variables. I use dithiopyr when the forsythia bloom then a sequential ap around now for poa annua and winter annuals. Agoodnap is spot on with mesotrione (tenacity) which can be used at seed down and for an overseed. Tenacity has both pre and post emergence; it might require a second ap. Note the other pre-emergents I mentioned can not be used in overseeing for 2-3 or more months. As a post emergent, something with quincloric or 24d (e.g., Orthos with crab grass preventer). But the best way is a good PM program. I would not use roundup unless you want to kill desire able turf that you might accidentally spray. A full renovation--killing everything and reseeding--can give you great results but is a lot of work and I wouldn't do it unless you know what you are getting into. You can get these products online or at something like a John Deere Lanscape. You really need to read the label or whatever you use. Last thought, don't skimp on seed. I would not buy or use seed that has any percent of weed seed or "other crop."