They should:
1. Greet you,
2. Ask "are these your personal effects", and
3. Ask for your permission to search your effects.
You can refuse which will mean you cannot proceed past the screening point.
Once you permit the search to take place, the item being searched remains under control of the screener not the person who is being screened. Therefore the search will generally take place out of your reach.
They are also required to ask your permission before subjecting you to an explosives trace detection (ETD) but are getting lazy these days and just call you over and begin testing you and your bag.
Specifics of the procedure are contained within the aviation screening notices which are not published.