Most airlines have set procedures and are found in their repective procedures manuals, suggest you go and ask for them from them.
Some airlines insist on an engineer being on the headset for obvious reasons.
Some examples of exchanges -
FD - No1 engine won't start
FD - I have an EICAS Advisory/status .......
FD - No N1 indication
FD - I have RF on no4 hydraulics
FD - I've lost VHF L & C
You must know the basic handsignals which can be found in various manuals.