If you are speaking out loud to someone and using something like, "I said," you will use quotes. However, you can convey conversation without quotation marks. Here is an example of a dialogue which uses some different ways to convey the information:
Jennifer told me she was tired of seeing my bright blue shoes every day.
I said, "I don't make enough money to buy a new pair!"
Laughing, she said, "Well, why did you choose that color in the first place?"
Looking at the grey and black shoes she always wore, I thought that I could have asked her that same question, but I decided it wasn't worth stirring up trouble. "I guess I just don't have your good taste," I smirked.