I only know a few bits and bobs, and some of these aren't exclusive to Manchester, but I know they're used there.
A cup of tea can be referred to as a 'brew', as in "Make us a brew, will you?"
My Manc friend refers to her brother as 'Our Kid' (when he annoys her, she refers to him as a 'cocknobber')
If something is good, it's 'mint', 'sound', or sometimes 'dead good'.
If something is bad, it's 'cack'
To hit someone is to 'lamp' them