Check out the various samplers from the better internet dealers, like JR, Cigars International and Holt's. Avoid Thompson's like the plague!!! Read the descriptions, and just order some. Keep a log of what you liked, what you didn't and why. That will help you refine your future selections.
Three pieces of advice:
1. Never judge a cigar based on a single stick. You are dealing with products made from natural materials by hand that are sensitive to environmental conditions. There is simply too much possible variation from stick to stick to make a valid judgment based on just one.
2. Wrappers and sizes/shapes have an astonishing effect on flavor and smoking characteristics, so don't judge a particular brand line based on just one size, and remember that the wrapper will change a cigar's flavor greatly.
3. Remember that your taste will change over time, so don't be afraid to revisit sticks that you tried but didn't like, and don't be shocked if you find that you don't like cigars that you used to love.
It's a great ride --- enjoy it!