First, go to the screen with the "Gears" labeled Draft, and pick Teams & Draft Order (see screenshot below)
the Edit Teams and Draft Order screen allows you to both edit teams and change the draft order
the Edit button you see in the menu is only for renaming teams and changing other team settings as seen in the screenshot directly below this paragraph. It is not for changing the draft order
If you press Edit and see the menu shown above, you will not be able to trade picks. Return to the previous menu shown below this sentence
Changing draft order should be done using the select menus on the list of picks between the pick number and EDIT on the screen shot above. Tapping any team's designation in the box to the left of the EDIT button, will bring up a menu of other teams to assign the pick to.
If any league has multiple picks in the same round for the same team, or any pre-draft pick trades, they should use the Fully Customized Order option instead of "Serpentine/Snake" - click next to Serpentine/Snake to switch to Fully Customized
In the fully customized order setting, any pick can be changed to any team for the whole draft.
To find later round picks in the draft, scroll down the screen showing all the team's draft picks (1.01, 1.02, etc.)
Hit the Green DONE button when all your draft picks have been arranged to represent the pre-draft trades to date