When you watch any work of recorded fiction on screen, whether it's TV or movie, it's extremely unlikely that you're seeing the first take of any individual scene. Scenes are shot and re-shot, with different focus and different emphasis, over a period of many hours. Sometimes, the same scene can be recorded over and over again for days. In the case of 'Saving Private Ryan' and the famous Omaha Beach scene, that period ran into weeks.
Every day, they filmed the scenes again, moving a little closer to the beach each time. Spielberg and the producers wanted the cast to get the real feeling of frustration, slow progress and physical exhaustion that came with this kind of warfare. When all was said and done, the actors involved in that scene had been at the beach every day for four weeks.