You can engage new people by asking them a question. say, you want to know the best place to eat around campus, so you ask a person about it and add questions like "why do you like it?" and "what is your favorite thing there?", then once you have taken their suggestion to eat there you could engage them later, "Thanks for recommending that place to me, it was good!" - Eventually you will find people who really enjoy talking to you and want to be your friend. :)

This question would probably get more responses in the "Discussion" section. I think normally Americans will choose to talk to people they already know. If they want to meet new people or join new groups the most common way to do that is through the friends they already have. However, especially as a new student in College or as a new worker at a job, it's not unusual to just walk up to a group of people and introduce yourself. This is especially true if you hear the group talking about something that you have a shared interest in.