Mister Slime is all about the mechanics. Moving around the world is done by tapping on anchors, which causes an arm to go out and grab it. In order to let go of another anchor, you simply tap the stretched arm. So moving from one side of the screen to the other involves clicking on anchors closer to your destination and then letting go of anchors behind you.
When you let go of all of the anchors, Slimey falls to the ground and rolls about (which feels vaguely like Loco Roco). While you can't really control Slimey like this, you can throw him forward a bit by grabbing onto anchors near you while you are rolling fast and slinging yourself forward a little, but there isn't any real power behind this so you won't be making a lot of progress this way. But don't worry, you will quickly learn how to catapult yourself by grabbing a pair of anchors and pulling Slimey back; so while this doesn't help you when rolling about the level's floor, you will be able to do some nice sling-shotting action.
Other things like opening doors involve tapping on Slimey's head and dragging an arm out (if you have one available) and grabbing the door (or bucket, or switch for that matter). While this all sounds pretty odd, it works out fairly well, and when you really get into it, moving around becomes very smooth.
Besides simple movement, you will eventually be able to use powers taught to you by Axons. In order to activate these powers, you will just have to draw different shapes on the screen. The game also uses the microphone to let you create a wind for Slimey to fly on, as well as having you flail about his arms in order to propel him underwater.
Mister Slime has a few issues that can get annoying in high concentration, but besides that, it is a really strong attempt at creating a truly unique and original game that uses the DS' touch screen to create an experience that hasn't really been seen before. If you are looking for a fresh experience, and don't mind the rough edges, then check out Mister Slime.