To find this feature, go to Google Maps, search for an address (e.g.: Madison Ave, NY) and you'll see a new option in the left sidebar: "Can't find what you're looking for? Add a place to the map."
You can also edit the details from existing listings and even remove places from the map. Among the possible reasons why you could delete a place you can find: the listing is a duplicate, the place doesn't exist, it is permanently closed or it's not of general interest. While business listings are changed almost instantly after you edit them, they can be removed only if someone from Google accepts your removal request. Each local listing can have a status like "Added", "Edited", "Removal requested" and the changes history is available to everyone.
Until now, only business owners could add places, using Google's Local Business Center. "We gather business information from numerous websites, Yellow Pages directories, and other sources to populate Google Maps search results. If you'd like to be included, you can easily enter your information into our online Local Business Center for free. (...) Once you've submitted your business information, you'll need to verify the listing before it goes live. You can verify using a touch-tone phone, SMS, or a PIN that will be sent via regular mail to your business address. Once the listing is verified, your information will normally appear in our results within six weeks," explains Google.
It's great to trust your users, but the places added using the new feature should be verified to make sure they are real. Turning Google Maps has a lot of practical advantages and could be used to keep the geographical information up-to-date.
Update: Google says you can edit places from the US, Australia and New Zealand.