This is based on my experience working as a production line pilot at Bell (that was over 20 years ago, but watching the folks at Mirabel as recently as 3 years ago, it hadn't changed much). I also watched it being done at Agusta in the US and in Italy. Basically the same process.
The process for accepting a helicopter off the assembly line is obviously different for each machine, but in general will be a very disciplined process that involves checking every aspect of the machine for proper operation.
All snags will be noted and rectified prior to release. All the companies will have very tight quality control systems - it's their reputation that's going out the door!
It will start with ground runs to make sure things are right in general. Every system will be exercised, all temperatures and pressures have to be in the correct range, have to stabilize, etc. Radios will be checked for correct functioning.
Once all the things that can be checked on the ground are OK, then track and balance of the rotor is done. (obviously some things are done concurrently). Then the airborne systems checks for rigging, systems operation, and so on are completed. And when everything is OK, the aircraft may be flown for several hours to make sure it all keeps working. I think Bell insisted on 5 hours on the airframe prior to delivery just to make sure things are working properly. Everything that was a problem gets documented and fixed.
Now the customer comes in, and if they're smart, they'll go through everything with a fine tooth comb. Power assurance / topping checks, systems integration, and so on. Major customers often have a wonderfully detailed checklist and can (and should) be pretty demanding. They are after all spending quite a bit of money!
Hope that helps.