Faking IDs on a scale necessary to influence a presidential election, without being detected, would be a bit more difficult.
The physical ID manufacturing isn't the hard part and never would be. It's finding the identity you're masquerading as and then actually standing in line at a voting booth.
http://www.powerlineblog.com/ed-assets/2016/08/Mandella-Regi...
That's just a lack of creativity. A popular mechanism in the past was the false-bottom ballot box (the man who first brought that to SF in the 1800s was rewarded handsomely, reported by Irving Stone).
You can have ghost voters, for example. People registered at addresses that don't exist, then bus people from precinct to precinct voting multiple times. Also, people register to vote in two different places: http://www.slate.com/articles/news_and_politics/politics/200...
I have seen foreigners vote with my own eyes. I don't know how common that is (or any of it is, actually), but that is something that happens.
How could you possibly know they're not entitled to vote? Did you know them personally? Were you aware fully of their immigration status?
You listed two possible ways in your post.
EDIT: To be clear, I am asking specifically how you know you saw people who were ineligible to vote voting. A follow up would also be why you observed this and didn't tell anyone.