Sort of like eating an Oreo, everyone has their own way of reading The New Yorker. I like to read in bed but I often read at the bathroom counter while drying my hair in the morning. Sometimes I put the latest issue in my computer bag, but I can't recall ever having the time to read it while I'm about during the day.
I start at the beginning and go straight through. I skip all of the political articles and some of the Middle East fiasco articles. If an issue seems particularly uninteresting, which is rare, I just start looking at the cartoons. I often skip over the fiction and come back to it later. I try to discipline myself to read the poems which are usually quite good.
Then, when the new issue comes, I drop the old one by my bed and start the new one. Otherwise, I'm not up on the latest news and happenings, which would be a disaster!!

The half read issues pile up until I lose my job or get sick. Right now, there are only two issues by my bed! I feel very efficient!!
I take old issues over to my mom's retirement home, where the residents look at them like they are made out of some poisonous material.