I have been a java developer for 2 years.
But I have never wrote a WeakReference in my code. How to use WeakReference to make my application more efficient especial
Using a WeakReference in Android isn't any different than using one in plain old Java. Here is a great guide which gives a detailed explanation: Understanding Weak References.
You should think about using one whenever you need a reference to an object, but you don't want that reference to protect the object from the garbage collector. A classic example is a cache that you want to be garbage collected when memory usage gets too high (often implemented with WeakHashMap).
Be sure to check out SoftReference and PhantomReference as well.
EDIT: Tom has raised some concerns over implementing a cache with WeakHashMap. Here is an article laying out the problems: WeakHashMap is not a cache!
Tom is right that there have been complaints about poor Netbeans performance due to WeakHashMap caching.
I still think it would be a good learning experience to implement a cache with WeakHashMap and then compare it against your own hand-rolled cache implemented with SoftReference. In the real world, you probably wouldn't use either of these solutions, since it makes more sense to use a 3rd party library like Apache JCS.