Here are the steps for better cornering on a mountain bike for beginners.

lean in - lean into the turn.  This is really basic but there it is.

shift back - shift your weigh a little bit back.  Why?  Because when you shift your weight back you put more pressure on your rear tire.  With more weight on your rear tire it will be less likely to slip out from under you. 

pedals even - Keep your pedals even going through a turn.  Why?  Because with the inside pedal down it's possible for it to strike a rock, root or the trail, and even pedals provide more stability.

look ahead - Eyes up.  Don't watch your front tire, Watch the trail.  Look at the turns that are coming up and plan your approach instead of having to make something up at the last minute.

front brake - braking on a mountain bike is counter intuitive. When you're braking on your mountain bike use mostly your front brake.  The proportion front to rear brake application is about +65% front brake. Using your front brake will stop your more quickly and you will have more control over your mountain bike.  Why?

Before you enter the turn you should be sure to slow down your bike enough so that you won't have to use your brakes too heavily during the turn, as this makes it more likely for your tires to wash out - lose traction  - and makes your turns more difficult and not as fast as they can be.  As a beginner speed may not be your objective, but you should still use proper technique regardless of your goal.