I've cycled 1 gallon tanks before, but I agree with the others, it's generally best to do 100% water changes.
However, if you still want to cycle your tank, this is what I did:
Add 5 drops of ammonia every day until nitrites spiked.
After nitrites spiked, reduce amount of ammonia to 2-3 drops a day.
Wait until ammonia and nitrite readings are both 0.
Do a LARGE water change to reduce nitrates.
Now you can add fish.
NOTES: You need to have either substrate (gravel or sand) or a filter for both to work. To speed the cycle up (it usually takes 2 weeks), add established material (ie. substrate or filter media) from another tank.
Remember, you'll still need to do water changes every couple of days.