The are 2 different ways across 2 unique modes of transportation to help you travel from Dortmund to DTM. If you're only considering the price, you should check out the train out of Dortmund towards Holzwickede, as it is the cheapest to DTM. It's common to find tickets for as low as $139. Train from Dortmund to DTM, it will get you there soon enough!
There is usually no need to book these sort of trips from Dortmund to DTM in advance. Rideshares should be available on demand all hours of the day.