You've got the absolute basic necessities in there now, so you can activate your theme (although, it won't look like much yet). Log in to your wp-admin, and navigate to Appearance. There, you'll see your theme waiting for you. As you can see, I've created a nice screenshot for my theme, with the name of the theme on it for easier identification:
At this point, you can activate your new theme and continue working on it to include WordPress-generated content and make it into a full-fledged WordPress theme in general. Don't be alarmed if the theme doesn't look perfectly right after activation, though. There's still some work to do. This is another good reason to have a development server. You wouldn't want to have this incomplete theme active on a live site while you finish the final pieces in the background.
Note that not every theme installation goes as expected. Sometimes, you have to deal with errors. In most cases, WordPress will let you know what went wrong with a notification. Every once in a while, however, activation can result in a critical error and your whole site could go blank. If that happens, simply rename the new theme's directory, or delete it completely. This will force WordPress to switch to the default theme, and things should go back to normal. From there, you can start looking for the issue that caused the crash in the first place.
Speaking of final pieces, your theme is now ready to have all of the WordPress content added, so let's do just that!