How can I measure the return and benefit of a commercial/advertisement after it's been published?

That is the mother of all questions in marketing and answering this question can fill a book.

Shortest answer says it depends on the medium and on the measure - in other words on what you mean by "return" and "benefit" (sales lead, sale, awareness, likeability, image increase etc etc)

One of the most valuable elements for marketing is the ROI that is generated from the campaign. ROI for any marketing campaign can be calculated using below thumb rule:

ROI = (Campaign Revenue - Campaign budget) / Campaign budget

Further if we break down the calculation of the Revenue generated, it's directly derived from the below:

Campaign Revenue = Leads converted * Unit price

Now, the leads converted are a direct derivative of the total leads generated from the campaign (commercial/advertisement etc.). The most efficient way of capturing leads is to include a Call To Action (CTA) in the campaign creatives - it could be a toll free number or a landing page link that can be included in the creative or a combination of the two. Once the consumer responds to the CTA, he/she can be filtered further based on which campaign they are calling from (newspaper/TVC/radio etc. - depending on the number of campaigns running in parallel). 

Clarity about this flow & relation between marketing vs revenue is the most vital element of any campaign, digital or offline. Once the ROI is calculated, it helps in the post-campaign analysis and can be a valuable guide on future campaigns & budgets to be allocated for them.

It is important to correctly attribute the benefit of various marketing tactics. Using unique promotion codes can help. For digital, ensuring proper "tags" for tracking should be in place. You can always go down the more expensive path of implementing Attribution Models.

There are measurement metrics by which the ROI can be measured if this is an tactical campaign. Any brand campaign the objective is to create awareness and making announcement. The same measurement metrics do not work for the same.

Our colleagues have already answered this  in theory of marketing and advertising

I'm assuming that this question relates to a specific campaign that is "published" on a mass media with no metric tracker  such as billboard, Print media, or TV(hence the question)

In my experience what we do to check if such campaign has any effect is to compare leads generated from the date of publication till end of publication.  compared to previous month/s AND the same days of the prior year.  Factor in other activities that may affect the analysis and you will have a control and a variable metric that would show a difference in leads/sales with and without the campaign in question.

I Can measure through the serve of selective customers that our tvc better or not