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Here is an implementation in JS

//3.5 Implement a Queue with Two Stacks
var stack = require("../../../lib/dataStructures/stack.js"); 

var stackQueue = function() {
    this.popStack = new stack();
    this.pushStack = new stack();
    this.length = 0;
};

stackQueue.prototype.moveToPop = function() {
    while(!this.pushStack.isEmpty()) {
        this.popStack.push(this.pushStack.pop());
    }
};

stackQueue.prototype.moveToPush = function() {
    while(!this.popStack.isEmpty()) {
        this.pushStack.push(this.popStack.pop);
    }
};

stackQueue.prototype.push = function(data) {
    this.moveToPush();

    this.pushStack.push(data);

    this.length++;
};

stackQueue.prototype.pop = function() {
    this.moveToPop();

    this.length--;

    return this.popStack.pop();
};

stackQueue.prototype.isEmpty = function() {
    return this.popStack.isEmpty() && this.pushStack.isEmpty();
};

stackQueue.prototype.peek = function() {
    this.moveToPop();

    return this.popStack.peek();
};

module.exports = stackQueue;

Queue can also be implemented using one user stack and one Function Call Stack.
Below is modified Method 2 where recursion (or Function Call Stack) is used to implement queue using only one user defined stack.

enQueue(x)
1) Push x to stack1.

deQueue:
1) If stack1 is empty then error.
2) If stack1 has only one element then return it.
3) Recursively pop everything from the stack1, store the popped item
in a variable res, push the res back to stack1 and return res
The step 3 makes sure that the last popped item is always returned and since the recursion stops when there is only one item in stack1 (step 2), we get the last element of stack1 in dequeue() and all other items are pushed back in step 3.

I need step wise algorithm for implementing que with using single stack