How do I evaluate the effectiveness of an advertising campaign?

The most important criteria for evaluating the effectiveness of advertising, depends on a many factors such as the advertising goals (if they are met) the type of media used, the cost, the value of the advertisement and the budget.

A recall and recognition test can be administered to a sample group or a random sample.
A recall is asking people who go to the mall what ads they remember.
And a recognition test is showing them a sample and asking if they recognize any.

Ask yourself if you would run a similar campaign again and why? If you can address this question in a SMART way: Smart, Measurable, Attainable, Relevant, Timely campaign then you should be able to measure its effectiveness.

When it comes to "Online", when the conversions are clear (for example, successful registration, purchases or any call-to-action indicating a positive result has been set) the best way to do this is to run different online campaigns (Different contents, creative...etc) and test them.
then start slowly eliminating the least performing ones to increase the CTR (Click through rate) for the best performing ones.
The only way to measure the effectiveness of offline campaigns is to provide a proper call-to-action and what they call a "Driver" which calls the customer to do something like fill a form, try a product...etc.

Impact and Sales figures.
The effectiveness of a marketing campaign can only be measured by whether or not the end-result was met.

External side : survey for the campaig durning and after with random sample of the existing and potential customers concernig  taste of  The message of the campaign, feedback about the product , the effectiveness on purchasing decision 

internal side : evaluate the campaign if its met the advertising goals ,product positioning , sales force , cost of the tools we used for the campaign vs return .

I think the effectiveness of an ad campaign could be evaluated before, during, or after a campaign.
A pretest would attempt to evaluate the potential effectiveness of the advertising campaign using, for example, a panel of actual or potential buyers who could judge one or more aspects of the campaign.
During the campaign, effectiveness could be measured by looking at actual customer behavior, while after the campaign is over, a company could use performance outcomes (such as sales or market share) to determine the campaign's effectiveness.
If I were to measure the effectiveness of an advertising campaign, I'd evaluate effectiveness at all 3 stages.

The objective of any advertising campaign is to sway perception in your favor.
Most of the time, this can easily be measured in terms of sales or market share.
However, not all messages require a purchase to be effective.
I believe this is where social media comes in: to get feedback directly from the consumer/target market.