How do you explain the evolutionary theory, especially transitional fossils and organ development, to an ardent science denier and creationist?

First thing (when discussing with a creationist) is to avoid any mention of transitional fossils… or any type of evolution that occurred in the past. Historical evolution is a terrible way to discuss the topic as it instantly challenges ideologies. you need to address real, factual changes that have been observed in the current time, changes that are not debatable.

The goal here is to create an understanding of the process occurring in nature… right now. Think on it, why doe sit matter if evolution occurred 20 million years ago to the average person? it doesn't. We need to know how it works now and into the future. The goal of someone admitting it has been occurring for 5000 years is sufficient enough to matter for the majority of what we need to understand. This is how farmers work with breeding, they do not need to know whether a chicken used to be a dinosaur… only what happens if they mix brown and red chickens is all that matters. Evolution on a large prehistoric range is relatively irrelevant.

Focus on the present evolution instead. Look at the modern adaptation of animals that are occurring in the world around us, this could include changes in domesticated animals and crops.

Stop trying to disprove people or force an opinion on people and focus on the relevant applications of knowledge. If they need to then they can worry about fossils and so forth if they choose to think harder on it.