The best way to play fast is to practice slowly.
One of the biggest mistake students make during practice is playing their music too fast. Slowing down the music allows our brain to process the information so that we can play the notes accurately, thus ensuring we play the correct notes. I know how tempting it is to play fast or to play the music as fast as we have heard on a recording. However, if you want to truly learn the notes to a song, you must practice it slowly. Once you are able to practice that specific part of the song (or the entire song depending on how far along you are), then you can gradually speed up the tempo.
It takes focus and persistence to slow the music down enough so that all the notes that are played are accurate in pitch and rhythm. Remember, learning to play an instrument develops many parts of your brain. Not only will you be making music, you will be developing and strengthening skills such as focus, memory, and persistence.
So keep your practicing slow and you will be on your way to musical proficiency in no time.