Use acronyms. In order, the lines on a treble clef staff represent the notes E, G, B, D and F. "Every good boy does fine" is one of the more popular ones. For the spaces, the notes are F, A, C and E, which spell the word "FACE."
Learn the notes in small bits. For some, acronyms aren't the best way to learn. Start by learning the first line and space in the treble clef staff. Play the notes over and over. Once that you feel you have mastered that, move on to the next two.
Learn a simple song. "Mary Had a Little Lamb" is a popular staple that helps beginner treble clef readers grasp the concept. Eventually, you may increase the complexity of your song selection as you get comfortable.
Practice scales. A scale is a climbing and descending pattern of notes that spans an octave. There are a variety of scales with varying degrees of difficulty, but don't worry about the complex scales. At your own pace, choose a simple major scale and repeat it until you are comfortable.