I was raised with Gloria Steinem's definition of feminism shaping my understanding, and have called myself a feminist since I was a child:
"A feminist is anyone who recognizes the equality and full humanity of women and men."
A more modern and inclusive version of that same idea, adopted by UN Women:
"Feminism is the belief that everyone, regardless of gender, should have equal rights and opportunities."
Feminism is a very complex grouping of movements and ideologies, but I think "membership" within them is very simple: if you believe in equality regardless of gender, you're a feminist.