If I search for a product name on Bing, for example "paint.net", the first result is something that looks like an advertising area, but it's called "Official Site".
How is it possible to get something like that for my own products?
At least not by forcing it. The feature is called Best Match, and it's driven algorithmically.
That post has an overview of what it does, etc. then scan in the comments for one from Bing at 6/24/2009 10:17 AM for a little detail on how something ends up in that area. Basically, you need to get people visiting your site from search results a lot in order to do it. Which is probably what you're after wanting to be there in the first place, so it kinda makes sense.
You need to sign up to Microsofts AdCenter.
Like Google Adwords, AdCenter is based on a Pay Per Click Advertising model where you pay only when they click on the link and visit your site.
The Cost Per Click (CPC) is based on a variety of factors including but certainly not limited to: relevancy, Click Through Rate (CTR), speed of landing page.
Microsoft search advertising is based on a pay-per-click (PPC) cost model. You determine your base bid, which is the maximum amount you’re willing to pay when someone clicks on your ad. You’ll never be charged more than your base bid and you might even pay less. With search advertising, one cent more than the next highest bid guarantees your ad is displayed.
More information is available here: Advertise on Bing using Microsoft adCenter