You'll use the +New Draft button that you see when you click the Gear button labeled "Draft" at bottom of your mobile phone screen, see the graphic below:
Starting a New Draft in Draft Dominator Mobile - Phones
Go over to the far top right of your screen and select +New Draft. See the graphic above at top right.
You'll see a menu like the one pictured below:
If you want to do a new draft in an existing league, simply click on the league you wish to draft in and then name the new mock draft:
Name this mock draft for the league you are practicing for - "Crazy Train Wreck League", or whatever. There are two levels to tracking your various practice drafts - you name each individual mock draft that you will perform under this league name. If you are practicing for different draft spots, you could name the various drafts as "Drafting from 1.05" or "Drafting from 1.07" to keep track of which mock draft results occur from those starting spots in this particular league. You enter the draft type and name in the box below the league name. When you are finished, click the green "Create Draft" button at bottom right of your screen.
The Draft Dominator can take you through multiple mock drafts for each league you are preparing for - so you can see what happens if you take Le'Veon Bell at draft slot 1.04 vs. Antonio Brown at 1.04 (and so forth). As long as you have saved the league settings once, you won't have to go through the setup process for each mock or live draft - in future, you'll just click the Gear button -> + New Draft -> click league name -> and then type in a draft name. So using the Le'Veon Bell example the draft name might be "Drafting from 1.04; LeVeon Bell" or "Drafting from 1.04; RB"
If you don't see the league you are looking for listed in the New Draft interface, you'll want to click the blue arrow labeled "Check For More Leagues" which will allow you to download new leagues created since the last time you synced Draft Dominator.
Also, you can manually add a league if you do your league draft in-person with a paper or free-standing draft board (thus, there is no league-hosting company to download from...).