Learned the treble clef when I spent two years sucking at playing the violin in elementary school. Learned the bass clef when I spent the next year sucking at playing the cello. Took this knowledge and taught m’self to play the piano, at which I do not suck. I’m an excellent sight-reader, which annoyed my last piano teacher to no end because in some ways sight-reading can take the place of practicing, but not enough to make the piece really good.
'Course, there was a while there when my ambition was to study music in college and become a film/TV composer. That didn’t work out, so now I’m in an even more moneyless double major. 
I learned to read the treble staff when I was 9 and taught myself cornet. My dad got me the instrument and a practice book and told me to sit down and play. I was like “Huh?” How do I work this thing? He explained “Every Good Boy Does Fine” and “FACE.” I figured out the fingering on my own.
I taught myself piano when I was 10, including the bass clef. After playing a lot of piano, I got to where I could sight read.
I never cease to be amazed at all the people who play proficiently and say they can’t read a note of music. But then, we don’t get amazed at people who can speak the language while not knowing how to read. It just seems like such a waste of musical talent to be able to play so well and yet not be able to read music. It can really make the approach to more complex stuff a lot easier.
When Van Halen first became big, I read an interview with Eddie where he said they all understood musical structures, so they could simply say “D seventh chord here” instead of having to go “uh, dude, you put your index finger on this fret on this string, and your middle finger on that fret on that string, etc…” I had to laugh because of all the teenage garage jams I’d been in where the other kids had to go through exactly that. I was so glad when my main jamming buddy finally learned scales, chords, and musical notation.
I can read treble clef - learned the clarinet for 10 years. For me, I read the note, and I know where to put my fingers, but I struggle to name the note.
I can’t read bass clef. Viola clef sends me into decline.