You need to work through each component and connection to check it's working. I suggest working backwards through the chain, starting at the amp, and following the chain to the guitar.
- Does the amp work at all? (you've proved this by plugging the guitar straight in)
- Do all the leads work? (try all of them, guitar direct to amp)
- Does the pedal output work? (plug it into the amp; since it's a distortion pedal, you should at least hear some noise if you crank it up. Some pedals can produce a signal without input, for example with a test button, or with the metronome built into some multi-FX pedals)
- Does the pedal input work? (plug something you know works into it)
- Does the guitar work? (you've proved this by playing it direct through the amp)
During this testing, check the volume controls on the component you're testing.
Work through these methodically, and you will find the problem.