You don't. And they're normally too busy doing their real jobs to waste time, or taxpayers' money, giving the film industry more publicity for its inane junketings than it generates for itself without their help.

The royal family's daily appointments are in that morning's edition of The Times. These are usually management meetings of charities they're on the board of: they typically arrive at the address in an unmarked car, and walk, unnoticed, to the office concerned. We leave the outriders and screeching police bikes to lesser nations, whose leaders need their fragile egos boosting.

There'll be a smattering of more public events: laying the foundation stone of a new hospital or opening a new bridge (usually hundreds of miles away from London). The details of this aren't published in advance, but if you turn up an hour or so beforehand at the location concerned, you might see crush barriers which indicate a public route.

Most often though, it's much the same routine as the charity meetings. A black Range Rover turns up, a royal gets out, acknowledges the two well wishers hovering outside, is greeted on the pavement by the hospital chairman then goes inside to do the biz.

They're best observed at major race meetings. Cheltenham Gold Cup Week more or less coincides with St Patrick's Day, though this year it's March 12-15

check the Royal Circular

http://www.royal.gov.uk/LatestNewsandDiary/Royaldiary/Locationsandtimes.aspx

http://www.nextaway.com/united-kingdom/london/articles/royal-wedding-tour-of-william-and-kate-s-london-haunts

Mid-March will definitely have "play it by ear" weather: whatever it is they might be doing might have a minimum of time outside for their sake and that of anyone who might have been thinking of hanging around to catch a glimpse. Often it won't include a period actually walking along and waving at the general public in the street, more inside with those connected with whatever hospital/school/theatre/worthy organisation it may be.

All you can do is keep an eye on
http://www.royal.gov.uk/LatestNewsandDiary/Royaldiary/Introduction.aspx

and hazard a guess as to how much "outside" time there might be when you see the weather for the day.

FWIW, the one reasonable certainty for an engagement next March will be the Royal Maundy service on March 28th next year. It hasn't yet been announced where it will be, I think, but it won't be in London, since that's where it was last year:
http://www.royal.gov.uk/RoyalEventsandCeremonies/RoyalMaundyService/Maundyservice.aspx