We love the atmosphere of the tailgate. You will run into a bunch of different groups. Some will be closed off, others will be very welcoming. If you are cool to the people you meet, just mingle and you should have no problem fitting in. This is very easy to do since you already know you are among Giant fans who are looking for a fun time. If you have something to share, even better... beer, chips, etc.
I travel over from Ireland to games each year and will also be at the Colts game. First time I went to a game I missed out on the whole tailgate experience because I wasn't clued in to what was going on. After that I decided to search for some different tailgate parties/groups on Facebook before going again. I got to know some guys and have been tailgating with them every time since.
Have a browse around online before going and introduce yourself and you will be made more than welcome when you go.