Hopefully, thus far, learning the guitar's strings more "formally", by knowing how they're transcribed onto paper in this Western music culture, has been not too grueling!
Let's move on to the 2nd string; the B string. You'll follow the same format of first learning the notes, and then applying the notes in an exercise.
Like the High E String, with the B string, you'll learn 3 notes to start off, in open position. They happen to be on the open string itself, the 1st fret, and the 3rd fret. Those note names are B, C, and D, respectively (notice how the note letter names always ascend alphabetically?)
Now, in greater detail, here are those 3 notes again. Starting below with the B note, plucked open, with nothing fretted.
Next, on the first fret you'll use your pointer finger to fret the C note.
Finally, you'll use your third finger to fret the D note, on the 3rd fret.
Applying those concepts, try working through the exercise below, using the diagram above as a guide.
Your brain will begin to link the process of fretting the note, recognizing the sound, with the visual representation of the notes on "paper". This is ideal and what you want to happen.