Rule 1: If you're a league player, when you sense that a cue ball foul is imminent, call time and request a hit watch by a knowledgeable third party. (doesn't pertain to bar leagues - bar league players don't generally care about double-hit fouls. They just bang away.)
I play in two leagues a week, one APA and one TAP, and situations where a possible double hit on the cue ball come up often. If it's my turn, I usually turn to my opponent at these times and ask if wants someone to watch the hit. I leave it up to them. Often they say no need we can watch ourselves. I've learned this is a mistake and won't go along with this self-policing any more. Though often a double hit is easy to detect, sometimes, it's just too hard to determine. Get a third party.
I was playing a guy last week in the TAP league who thought he was slick. I was thinking to myself, if he plays that 7 ball which was about a quarter inch from the cue ball, I'm going to call for a hit watch. But before I could stop him, he took the shot without calling the ball - he just banged away. Well, I called the foul on him myself and took ball-in-hand. Of course, this nit said it was a good hit and that he shot at an angle. I said bullshit. The angle was about 3 degrees and the whitey flew around the table like no legal hit would allow. Besides, I saw and heard the double hit clear as day. Anyway, though it's against protocol, I wasn't going to let this guy get away with this shit. So, I called the foul myself.
Of course, old slicky was already on my list of dickheads from a couple weeks earlier. I was playing one of his teammates in APA while he was watching from the rail. I drilled his buddy 5-0 but after the 4th game while I was emptying the pockets and rolling them to the foot of the table, my opponent says, "The 3 ball moved." Well, the 8 ball was a wide open shot with no ball within 6 inches. So, I said, "What are you talkin' about?" He replies, "I'm not callin' you on it." And I reiterate, "What the fuck are you talkin' about. My shot on the 8?" Then he admits that he wasn't really paying attention but his friend, old slicky, had said something to him from the rail. So, like I said, I already had a low opinion of mr. slick.
Anyway, Dr. Dave has a video that explains pretty well the double hitting process. Watch it for your viewing pleasure: