Well around here in central FL, we have some climbs but most are short (big surprise) but can be steep (up to 14%). I generally diagnose the hill as a approach and plan my attack. I will generally spin up it until a reach a point and get out of the saddle to the top (if it is a steep one). I recall Thrill Hill was the only one I ever walked. It goes down into a narrow valley and you can hit over 40 on the descent. I looked at the other face and figured I could roller coaster it. So I went up in my big ring at high speed and down shifted to keep my cadence up. Then I hit the deceptively steep section which is probably over 14% for a short distance. I knew it was double shift and hope I nailed it or crash. I figured why risk it? I just stopped, got off, and walked the little way to the top.
On long climbs, I have done mountain passes in NM, UT, WY, CO, MT, Alberta and British Columbia. I generally like to use a bike with really low gearing so I can sit and spin the whole way up. Most of the western climbs are not that steep anyway. I believe the nastiest climbs are in the east. There are some roads in GA and NC that go about 28%. Some of them are sustained climbs at over 12%.
I think climbing is largely conditioning and pacing. If you really hammer up hills repeatedly, you can easily blow up in mid ride. Also, like Yogi Berra said "90% of it is half mental". I recall on one ride we did Trail Ridge Road in CO which gets over 12,000'. We were staying at a high school some ways south of the climb. As we headed into town, I got suspicious. For some reason, they like putting high schools on bluffs (they do that in MI anyway). I looked at the nearest bluff to town and it looked like a school up there. So I figured we would have a short steep climb to the school. And we did. I was mentally prepared for having the steepest section of road on the last mile. Most of the riders were caught unprepared. I had to be as beaten up as they were but being mentally prepared for the climb made it no big deal.