To manually input distances in The Conqueror App you need to follow these steps:
Log in to The Conqueror App.
In the main screen refer to the bottom left button as shown below.
Make sure you are in the Post a Distance tab and you will then be able to input your distances. You will need to select a date and Activity. Then, in the lower section it will show the challenges that you can post to based on the challenge's posting preferences. If you are trying to manually input an activity but your desired challenge does not show up, you would need to update the posting preferences for that challenge to accept that specific activity. To do that refer to the article by clicking here.