The idea behind 2-city NC is to build the NC quite quickly, say by turn 60-70, so you can resume dropping cities as quickly as possible. Works really nicely when you have calendar-based luxuries in your capital, since calendar is on the beeline path to Philosophy. Build an early library in your capital (or GL, if that seems attainable--easy on Emperor if you have a spare forest to chop) and rush-buy a settler for your second city. To get started on NC as quickly as possible, either chop a forest in your second city to rush your library there, or rush-buy the library.
Start working science specialists as soon as the university is up. You also need to keep growing, so if you are severely food strapped, you need to fix that as soon as possible (e.g., friendships with 2 maritime CSs will allow you to work 2 specialists in your capital on a food-neutral basis until the food bonus from Civil Service kicks in).