Ovi Store can be accessed from almost any Nokia phone by just going to store.ovi.com on the phone's web browser, but certain phones also have an Ovi Store application available which lets you use Ovi Store much more easily. Some people have managed to find the Ovi Store application available through the Download! icon, but it now appears that you can also download the app directly from the store.ovi.com website. The availability of the app seems to currently vary depending on which model you have and which country you live in, and the easiest way to find out if you can get it is to visit the Ovi Store mobile site and see if the link appears for you. See the screens below for details.
The Ovi Store mobile website can be reached by going to http://store.ovi.com/ on your phone's web browser.
Here's what the app download link looks like on the Ovi Store mobile website (you may also see similar links elsewhere on the site, for example near the bottom of the front page of the Ovi Store site). You'll have to sign in with your Ovi account before it will let you download and install the app.
Once it's installed, the Ovi Store application can be accessed by clicking on the Ovi Store icon, which is probably in the phone's "Applications" folder:
Clicking on the phone's Ovi Store icon starts up the Ovi Store application which makes it much easier to browse, download and install applications: