When you begin to combine trope with hebrew text, it helps to practice in small steps. First, read the passage carefully, using the correct pronunciation and accents. Second, sing the trope signs by themselves. Finally, once you are confident with the pronunciation and melody, you can combine the two.
Guided Practice: Torah Trope
Above is the first paragraph of the Shema. Each line has three audio files: one of the spoken hebrew, one of the trope, and one of both combined. Practice the passage line by line, then try them all together.