At the top of most pages on EcchiDreams, you'll find a small icon with three lines (called a hamburger button ≡) If you click on it you'll be presented with a menu, like so:
At the top of that tap on the smiley face icon:
Which will load this:
Tap on the icon you want, and it will add the text under that icon to the "Currently Feeling" box below, which you can then edit if you wish (up to 48 characters). Then tap on update, and that's it.
To remove the mood, just open up the moods panel and click "Remove"; that's it.