I'm in the process of learning to read music and play guitar. I have a book telling me if I play my second string open that it makes a B. Can anyone explain to me why it shows as a G on my tuner? And as I learn the second string all of the notes are wrong on the tuner??
The most obvious reason is that your 2nd string is actually tuned to G. That needs putting right. When your tuner is showing B for that string, then the other notes you play when fretting will show correctly on your tuner - assuming it's capable of showing all notes and not just the 6 open guitar strings. I hope it's tuned to a low G, 'cos it could just be tuned an octave higher, and will be rather tight. Check your G string is correct, press it on the 4th fret, look at your tuner. It ought to read B, exactly the same note as your B string open.
Most electronic tuners will display the note closest to the frequency being detected when you pluck a string on your guitar. So if your second string (which is the next to thinnest string on a six string guitar) is tuned closer to G than B, your tuner will display G.
It's important to tune each string to the correct octave of the pitch it is supposed to be tuned to. In other words, if you attempted to tune a string one octave higher than normal, it would likely either break or in the case of your heavier strings, place a potentially dangerous amount of stress on your guitars neck.
It's best to start with a reference point such as a friend's in-tune guitar, a piano, a tuning pitch pipe or online tuning site.
Since you obviously have access to a computer, go to an online guitar tuning site such as Fender online guitar tuning site or JamPlay Online Guitar Tuner Use one of these sites to match your strings to the pitch you hear on the site for each string - to get you in the ballpark. Then use your digital tuner to fine-tune to the exact pitch.
Good luck and have fun learning to play the guitar.
Make sure that you are counting the strings starting from the highest pitched one (also the thinnest, and the bottom one if you are holding a standard right hand guitar pointed to your left). It seems likely that you are counting in the opposite direction and playing the A string, which has gone flat and is sounding closer to a G.