I was told that the worse way to build your credit score was with a credit card?

Someone told me that it was just a scam the credit companies started to try and get people to get credit cards. I'm 22, I go to school full time and work 30-35 hour weeks. I do not have any tuition loans, I pay for my college out of my own pocket. I've been trying to build my credit score with a credit card that I got from a credit union. I was doing good for a while. Like I'd buy little things and pay the whole thing off. But, lately I've been putting about my whole paycheck towards paying the card off every month. I gave the card to my dad so I'd stop using it. It's almost paid off (just a $300 balance left). Someone told me that the belief that having a credit card to build my credit score is just something the credit card companies made up to get more people to open up cards? But, how the heck could I build my credit score up if I can't even get a loan without a co-signer? (I don't like having a third party involved in my finances) I really want to build my credit score because I'd like to buy a car after I graduate and I know I'd need a small loan. Any suggestions?