Very basic singly linked list
size++ should be extracted from both branches and called only once
there is no need to cache instance variables where local method variables should be used instead: newNode,oldNode,displayNode
prefer while(currentNode != null) over while(true) and currentNode should start with firstNode and be chained inside the while-loop as currentNode = currentNode.next
you should also provide remove and iterator functionality
DisplayLinklist should not be inside this class and it should be camel cased
variable firstNode is usually called head
class linkedlist should be called LinkedList
get rid of unwanted blank lines