Hi! I saw him cross the street - it means, you saw how he finished the action. I saw him crossing the road - you saw him in the process, but you don't you if he finished it.

Marina gave a correct answer. If you have the famous grammar book English Grammar in Use by Raymond Murphy, consult Unit 67. Here is a related italki discussion: https://www.italki.com/post/question-470450

Hi i’am nisreen from palestinien i want anybody to help me talking English well I will be greatfull Thanks

Hi Tomas, the first sentence would mean that you basically did not see the whole process. The second one means that you saw the subject from the start to the end of the action. Which was, in this case, crossing the road.

They are basically the same. There is a slight difference in tone. In my opinion, "I saw him DOING" sounds a little more active than "I saw him DO." But the overall meaning is the same.