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It's obviously easier to get into a film if you live in a place where a lot of movies are shot (like L.A.). But in my friend's case, he took a college class that required travel to Manhattan. Perfect.
You can find the shooting schedule of various movies through online "insiders" websites or by looking at the fliers that movie crews leave around the city. Also, city film comissions have schedules of any filming that occurs. Or, have your friends stumble across the set and tip you off (my method).
On a nice Manhattan Sunday in the summer, my friend wore a wool suit to church, and a mutual friend told him where the set was.
He took the subway to the Spiderman 3 movie set.
Step 1: Show Up at the Set
Keep walking past the set, trying not to look interested (to gauge the level of security). Crowd scenes are your friend here, and this was a crowd scene.
Notice the fashion models boredly browsing the catering table, but don't take their pictures or talk to them, in case they get mad.
Borrow the port-a-john.
Then slowly walk back towards the set and nonchalantly take pictures of the surrounding buildings, the trees, anything but the set itself (to avoid looking suspicious, but still getting closer so you can see the set).