This is the tablature for Romanza, one of the most popular classical guitar pieces ever written. It is played using triplets in 3/4 time. In other words, play three notes in the duration of one quarter note. A good way to do this is to say Trip-a-let, trip-a-let,trip-a-let... while playing.
Three chord fingering you will be using are Am, and two forms of B7.