After making a sufficient research on the topic, I managed to build a solution out of two separate tutorials.
My main problem were the dynamic prototype cells used in the storyboard example provided by Apple. Therefore I created a customised cell with UIDatePicker inside. I used this tutorial to customise the cell xib file according to my needs and then used it in the UITableView.
Afterwards I followed this tutorial, only instead of a storyboard I created a UITableViewController and used the custom cell with UIDatePicker inside. This example seemed much easier to follow than the sample code provided by Apple.
I didn't encounter any other problems on the way, but if you have any questions I would gladly try to answer. I am still quite new to iOS and Objective-C, so maybe three is a better and easier solution out there.