Navigate to your inbox it will be the first screen when you open up the YouMail app.

From the drop-down arrow to the right of Inbox, you can select the folder where you would like to delete messages.

You can select multiple messages to delete by holding down on each one, they will gray out.

When you have selected all messages you wish to delete, press the trash can icon in the upper right corner (shown within the gray bar).

You can also delete messages by swiping the message to the right or by opening the message you would like to delete and selecting the trash can icon in the upper right corner.