There are direct regional express (RE) trains roughly every two hours from Berlin Hbf to Lutherstadt Wittenberg beginning at 6:32 am. Same story in the other direction beginning at 7:00 am. Those 2-hour intervals are peppered with additional journeys that require a change of train on the way.
You can look this stuff up yourself at the DB Railways site. Just click on "only local transport" when you do your search to find regional trains. Next year's schedules aren't loaded so just use the currently-available times as a guideline and check the actual times later.
For regional trains you do not book in advance (unless they are part of a high-speed rail journey.) You just buy tickets or day passes at the station. For this journey, the Brandenburg-Berlin ticket (day pass) is normally on offer and covers the round trip for 2 persons at €33 for trips this fall. I'd expect a similar day pass offer next year.