Once you are on the "Update Word Press" page, click the button "Update Now" to start the process off.
You shouldn't need to do anything else and, once it's finished, you will be up-to-date. If you have any problems, it is probably related to permissions issues on the filesystem.
See the tutorial on Changing File Permissions for more information, including how to configure file permissions so that multiple FTP users are able to edit the files.
If you see a "failed update" nag message, delete the file .maintenance from your Word Press directory using FTP. If the one-click upgrade doesn't work for you, don't panic! These are the short instructions, if you want more check out the extended upgrade instructions.
When a new version of Word Press is available you will receive an update message in your Word Press Admin Screens.
To update Word Press, click the link in this message.
Most sites are now able to automatically apply these updates in the background.
If your site is capable of one-click updates without entering FTP credentials, then your site should be able to update from 3.7 to 3.7.1, 3.7.2, etc.
You should always update Word Press to the latest version.Consider rewarding yourself with a blog post about the update, reading that book or article you've been putting off, or simply sitting back for a few moments and letting the world pass you by.Your update is now complete, so you can go in and enable your Plugins again.You should do this as soon as possible after step 1. If you have caching enabled, clear the cache at this point so the changes will go live immediately.Otherwise, visitors to your site (including you) will continue to see the old version (until the cache updates).