Listen to the song. Listen for repeating patterns. When you hear those patterns, attempt to play along. Most songs are based on a few repeating chords. Once you have heard these chords, and can repeat them, you will be able to attempt the rest of the song. Practice the chords until you are fully comfortable with them.
Listen to sections of the song, perhaps in 30-second bursts. Attempt to play along with a 30-second section. This not only improves your playing but also your ability to hear notes. Do not move on to the next section until you have mastered each 30 seconds. If it is getting difficult, focus only on the guitar — not the lyrics or drums. This helps you to concentrate on what you should be doing.
Use a heavy pick if you are finding the notes too fast. A heavy pick means that you can pluck the strings harder with less effort and that you can go from note to note faster.
Play the song through all the way. If there are parts that cause you difficulty, then you should practice these areas. Keep doing this until you are able to play the song all the way through at full speed.