I got a book from the library called something like "Toilet Train Your Child in One Day." It was from the 1970s and the cover and layout were very dated but it was a great resource! I didn't bother to campaign for a one-day training process since my son was like yours, just starting to show an interest, but I loved the approach of positive reinforcement. The basic suggestion is to offer a few salty snacks and treat drinks (becasue the more opportunities your child has to practice, the more opportunities there will be to reinforce success) and praise the child for staying "clean and dry," not for sitting on the little toilet or whatever you're using. . . as in, "Here's a pretzel for you--you are so big and you are staying clean and dry! You know how to use the toilet to stay clean and dry! You can have a juice drink!" This went over huge with my son because usually I'm all about water and healthy (read "boring") snacks. So the treats really had his attention and worked to give us more opportunities to practice. Using a baby doll to impress was also helpful and helped me hone my theatrical skills, ha, ha. (This time around I actually have a real baby for my middle boy to impress--no prop needed!) The book also details this aspect.
Learning to use the toilet was still a process, but I didn't find the process so burdensome. I liked that I was praising for the real result I wanted (cleanliness) not just a piece of the behavior (sitting on the toilet). It was gentle and positive and easy to be consistent with.
I'm sure you could find this book for very little on Amazon or Powells.
Good luck!