Operating expenses are those expenses which are essential to the carrying out the main activities of the business but not including Cost of Goods Sold. All the normal administrative and sales expenses are operating expenses. For example salaries, rent, commission, telephone, advertising and travelling expenses are operating expenses.
Non Operating expenses are those expenses which are incurred for non essential activities of the firm. For example for a firm manufacturing electric bulbs payment of interest is a non operating expense but for a Finance Firm it is an operating expense because for the former firm raising money is not its main business but for a finance firm raising funds and lending funds is its main business. Other examples of non operating expenses are cost of obsolescence, cost of currency exchange and payment for a law suit or amount spent on reorganisation of the business.
So to identify whether an expense or income is operating or non-operating is to see what is the main business of the firm. For example business of a firm A is to manufacture electronic goods, its rival, firm B files a law suit against firm A for copying its products. Firm a spends Rs.50,000 on defending this law suit. Though this expense relates to the business of firm A but it is not related to its main business of manufacturing and selling electronic goods. So, this is a non-operating expense. This is the way to judge whether an expense is an operating or non-operating expense.