THE INTERNET IS YOUR BEST FRIEND
Ok, so sometimes a travel hack involves just doing a little research. Why people don't do more research, I don't understand. When you walk by all those terrible, minging faces standing in line as you strut by gloating, you can't help but think to yourself..."why the hell didn't you use google?"
Or if in the very least you don't like to use Google, ask a local! Or someone at your hostel, hotel or airbnb. I stayed with a friend's mom's B&B in Rome, and Adele was an incredible host. I told her where I wanted to visit and she told me all the hacks. ORDER ONLINE AHEAD OF TIME. You can do this up to 60 days in advance. Yes, you do have to pay a few euros more (4) - but in the end it's worth it entirely! I walked by the equivalent of a block long line to cut to the front for my 1pm slot time and walked right into the Vatican Museum. I went during "off season" in Rome, so I was able to order the tickets about an hour and a half before. You can use visit the site by clicking here. Make sure you have to print the voucher out ahead of time.
After checking out the Vatican, you can just take a 5 minute walk over to the Basilica. The only line longer than Chipotle on a weekday lunch hour - but it moves fast. It didn't move fast enough for me though, so I just walked up confidently to about 1/3 of the way pretending like I was walking through the line, and then just stood there. This worked for me cause I was solo, but it might not work for a larger group. Try blending in with people that look like you. I do it all the time with Asians. "Hey, Can I backskip you?"
SIDE NOTE: If you forgot to buy your ticket online first, you can always wait on the shorter/ faster line for the Basilica. When you leave, there should be a little booth selling tickets to skip the line to the vatican. I'm not too sure about details - so check it out yourself.