I'm finding this was easier to do when I lived in a nonobservant and nonJewish community. The coworkers and friends I approached started by getting weirded out, but afterwards they said they actually appreciated the discussion. Sometimes I learned that what seemed a big deal to me wasn't anything they even remembered, but something I had forgotten seemed like a big deal to them.
Here in my frum community I'm finding this exercise somewhat harder. The one person I approached this year didn't let me finish speaking, but since told me I was forgiven (for what he had no idea) and asked that I forgive him for whatever (unspecified) wrongs he had done me. It was formulaic and very offputting.
I'd be interested in the opinions of my readership (all 5 of you :>). Do you do detailed apologies? Do people stop to listen to them? Do they serve a purpose in your eyes?