The DMFUtil class is a great code collection to be aware of in case you ever find yourself trying to kick off DMF import/exports via x++, or are just curious about how some of that entity stuff works.
The setupNewExecution method is the most convenient and succinct way you can create a new execution to kick off. First, all you need is the string name of your definition group, which could have been created manually or through code. Next, the ExecutionId is generated (and ultimately returned) via the mother of all ExecutionIds (you should check out the generateExecutionId method as well).
The DMFDefinitionGroupExecution::InsertOrDisplay method is the super helpful finale. If you peek in there, you'll see a lot of fussy work being done for you. Once you get your own DMFDefinitionGroupExecution record, you can do pretty much any DMF-related thing you want. My favorite use-case is calling the DMFDownloadDataPackage class to create a downloadable package: