Just get the mavericks seed configuration utility from the mac dev center, install it and then 10.9.1 build 13B27 will appear in Updates in the mac app store.
If it is not showing up in safari, use a different browser.
Then just download and install 10.9.1 from the mac app store. Don't forget to copy the installer somewhere before the computer restarts if you want to keep it, because otherwise it will delete itself.
If the mac app store isn't working properly, there is a direct link available in apple's developer forums (which unfortunately we can't post here because it would breach macrumors rules). If you download it that way with google chrome, you can double click and install.