While I remember there are drawbacks with local communications to and from the East Midlands Airport.
If you are using public transport to get to the airport, you have the following options:
OPTION 1) Take a train to Long Eaton or Loughborough station, Long Eaton is closer.
Take a bus, local service, stopping at East Midlands Airport.
Buses run at hourly intervals, the connection is a local service subject to delays etc.
Links: Traveline (buses), Trainline (trains)
OPTION 3) National Express coach direct.
Links: National Express Website
I opted for option one which resulted in incurring a £15 taxi charge (£5 less than the flight itself) in order to get to the airport on time.