You cannot know for certain which way an aircraft will make its final approach, or which way it will turn prior to it; local weather, especially ground level wind, is the most important factor. Air traffic control may redirect you based on other traffic, prevailing winds may shift, and so on. The most famous approach to DCA is the River Visual, following the Potomac River past many Washington landmarks, but depending on the wind, you may come in from the opposite direction entirely on the Mount Vernon Visual.
That said, some airports are more predictable than others. LAX is situated on the ocean, so almost all landings are to the west into the onshore breeze (whether your flight is directed north of the airport or south to turn is subject to conditions, of course).
Depending on the airport, you may be able to look up historical and realtime flight tracks on a site like FlightAware.com, Planefinder.net, or Radarbox24.com. From there you can make an educated guess, but there are no guarantees. Even LAX sees landings to the east when the Santa Ana winds are blowing hard.