None of these methods is foolproof. And none of them will work for all types of businesses. But try a few on your advertising efforts, and you'll get a sense of how well they're doing and whether the expenditure is giving you a satisfactory return on investment.
1. Mechanical measurements: When you have your customers bring in a coupon or a copy of an ad to qualify for a special discount, you have absolutely clear evidence of how well your ad has done. You can even code your coupons to the precise appearance (publication and date). This will also work with phone calls, when you code your ad with a particular "operator number" or have callers ask for "Mr. Henderson."