First, go to the menu under the "Gears" drop down box 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 screenshot above is only for renaming teams and changing other team settings, which is done on the right hand side of the menu. It is not for changing the draft order
Changing draft order should be done using the select menus on the list of picks to the left hand side of the screen shot above. Tapping any team's select menu (above, Team 5 has traded away his 1.05 pick to Team 6, so by clicking on Team 5 we then switched it to Team 6), 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 as pictured above instead of "Serpentine/Snake"
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, pull down the slider that divides the left half of the screen from the right half