Google calls this "campaign tracking" and their Analytics help site explains how to set it up. It's a two-step process:
Tag the links on your ads so that Analytics knows a visitor was sent from that ad.
Define a goal using your purchase confirmation or receipt page as the 'URL Destination', so that Analytics knows how many visitors hit the receipt page.
You can now discover what percentage of visitors sent by that ad ended up at your purchase confirmation page by:
- Navigating to the Traffic Sources > Campaigns page
- Clicking the appropriate campaign.
- Clicking the 'Goal Conversion' tab.
You can set up multiple goals to determine, for example, how many visitors sent from that campaign added the product to their cart or landed on the product page (Goal 1), and how many actually purchased it by landing on the receipt page (Goal 2):
Screenshot from this Campaign Monitor help page.
The above requires no modification of your website's source code, provided that your hosted platform already includes Google Analytics tracking code, that it offers a payment receipt page, and that you can modify the links on your ads to use tagged tracking links as described above.
More detailed Ecommerce tracking requires modification of your source code (or shopping cart software that supports tracking), which you say you can't do, but I include the link in case it proves useful for others.