First off I assume you are talking about the DA40TD (FADEC diesel engine) nd not the DA40 (non FADEC standard Lycoming engine).
The only thing you need to know to fly a FADEC equiped aircraft is the big knob(s) on the centre consol has 2 functions
1) Push to Go, and
2) Pull to Whoa
But seriously understanding how the FADEC works, or more importantly when it fails to work, is important. So for example a regular aircraft piston engine does not need any external electrical power to continue running, but the Thielert will stop if electrical power is lost even for extremely brief periods.
In general operating and emergency procedures will be different so you need to keep and open mind and not try to force previous conventional engine operating procedures onto this aircraft. Otherwise the DA40 is a pleasant flying aircraft without any unusual handling characteristics.