Without a mouse or a full keyboard, I'm not sure how I would use Mathematica Online.
- You can use Shift+Enter to evaluate a cell.
- Alternatively you can hover your mouse over a cell. A grey gearbox will appear. Clicking on this will give a quick menu that allows you to evaluate a cell.
These are the only easy ways that I know of to evaluate a cell. You can also evaluate a cell from the menu at the top of the notebook as well.
Maybe there's a feature for the IPad that will allow you to emulate having a mouse or a conventional keyboard?