Having spent the past 26 years of my life in this business, I've developed what I find the best way to deal with structure-dwelling squirrels.... in MOST cases. There's never a "best way" that fits ALL situations.
After identifying the primary access hole(s), I'll gang set near the opening(s) using open cage traps (open referring to non-posi sets). I do this for 2 days typically, sometimes 3 days. AFTER catching the bulk of the squirrels, then I'll install one-way doors over the holes.... usually without traps attached, leaving some cage traps near the one-way.
Reasons (determined through MANY years of experience): Installing one-way doors on the initial set-up OFTEN causes squirrels to chew in OR out, as they are neophobic and will do whatever necessary to avoid the excluders at first. I've seen them chew around one-way doors too many times, so that's never my first move. This sometimes spooks them, and they may leave the area for a day, or several days. THAT is a surefire way to cause an extended time period to solving the problem.
Same deal with entering the attic.... don't do it until after trapping. They are often spooked, and your trapping program will be ineffective for a couple days.
They are very familiar with their domain (structure interior) and any changes or activity (traps inside or you walking/crawling through the attic) can send them packing for a bit. They also do NOT forage for food inside, so inside traps will often go ignored for days. However, setting outside seems to greatly lessen their skeptical behavior, as they forage for food OUTSIDE. They will go to bait much faster outside than inside. Sometimes it takes a day for them to get used to the traps near the entry, but they get past the fear quickly.
After open trapping a couple days and another day or two of trapping with the one-way installed, the job is almost always done, except for the sealing/repair work. I use traps shelves which have small runners along one edge to help level them on rooftops. Holes are drilled for the Fields Development spring hooks to secure the traps. Makes for ultra-fast trap changes during daily visits. Takes a little longer to set up, but saves MUCH time in the long run. Trap shelves also keep the bait in the trap, on the floor behind the trigger pan.
Another major advantage of securing traps is the squirrels don't trip them from the sides. I have observed squirrels on many occasions "working" small cage traps. Especially in snow, they will try to get the bait from the side, wiggling the trap, often flipping it over or sideways, setting it off. Once I started setting my squirrel traps "solid", my "misses" were practically eliminated. Again, makes for more efficient removal of the animals. None of us have time to drive to job sites simply to reset traps that are empty.
I know guys who use nothing but posi-sets, but it takes them longer to finish the job as they get more call-backs. After a day or two with no catches, they pick up, and a few days later the "spooked" squirrels return, and the customer is on the phone pronto.... and back you go... repairing new holes and catching more squirrels.
Here's a pic from about 10 days ago... second day at a local squirrel job. Caught 4 the first day, 5 the second day, and one each day (for two days) after installing one-ways over the 2 holes. Noises stopped, job sealed up and done in 4 days. That's a normal scenario for my squirrel jobs. I had 6 traps set here. Guys who are setting one or two traps are NOT going to finish a job quickly. Never believe them when they say they only have "2" squirrels, because that's all they've ever seen at one time.
Same job, same day. Caught 5 on second day check. 11 total in 4 days, sealed, job done. That's my dad taking catches to the truck while I'm replacing traps on shelves.
Another job, this one in Woodriver, IL. I mounted this trap shelf at 11 AM. They were entering 2 holes, one on each side of the chimney in the soffit (chewed open). You can see where the homeowner tried stopping them with a 2x4, hence the new chew holes! Went to eat lunch a mile away at Subway, returned an hour after setting and had 4 for 4. Caught 13 from this tiny home. Seven the first day! This is not typical, but they really respond to bait and lure quickly in the coldest part of winter.
Of course trapping on the ground is almost never done (by me). I'm not there to see how many neighborhood animals I can catch, I'm there to solve a problem. When I catch high numbers within 10 feet of the entry holes, it's NOT neighboring animals. Chances are extremely high they are all using that structure.