I am an "early-career mathematician". I have been going to conferences for six or seven years now; my first conference/workshop was a week at Oberwolfach and it was absolutely wonderful. (Some of the food was odd: I did not know Germans loved curry and pineapples on ham and cheese, for instance. It was surprisingly tasty.) At that first workshop I drank two lattes a day from those coffee machines right outside the lecture hall, and beer in the evening of course. I attended every lecture faithfully and worked in small groups to understand the material. I learned a ton.
My first Joint Math Meetings was quite overwhelming. I was not interested in a particular special session so I ran around from talk to talk -- geometry to combinatorics to pedagogy to mentoring -- and chatted with people occasionally in the halls. I was a graduate student.
As a graduate student, I was a talk-attender: go to the talks to learn the math, right?!
Now I am a people-finder: go to conferences to find the people who might be able to answer that burning question you've got, and go to talks to hear about new fun things if you've got time!
Which do you do these days? What stage of your career are you at?