The process below is for upgrading WordPress software that is at least version 1.5.x or higher. Since the most recent version may vary, please refer to the official WordPress website before upgrading.
Step 1
Backup your database. The database is what stores all of your blog’s content from posts to comments. In order to back up your database, you will need to log into the database manager provided by your host. You may need to contact your hosting support for assistance with this process. However, make sure your database is backed up and in working condition BEFORE moving on.
Step 2
Backup all WordPress files. This is another essential step. Backup the entire contents of your WordPress install BEFORE moving on with the upgrade process. Double check to be sure all files are in workable condition. If for some reason there is an error with the upgrade, you will need to make sure you have these (the database and files) to revert back to.
Step 3
Deactivate your plugins.Leaving some plugins active while upgrading may cause problems. Access your plugins section of your dashboard and deactivate ALL.
Step 4
You should receive an update message in your WordPress administrator control panel "WordPress x.x is available! Please update now!"

Step 5
Clicking on the "please update now" link will take you to "upgrade WordPress page". Two options will be presented including "upgrade automatically" and "download x.x". For this example we will be using the "upgrade automatically" option. If you are choosing a manual install please visit the wordpress page for more information on manually upgrading WordPress

Step 6
After clicking the automatically update wordpress button you will be prompted to input your websites server details including hostname, username and password. This is your last chance to make a backup if you have not already done so (follow Steps 1 and 2 to make a backup of your site).

Step 7
Hit the proceed button and let WordPress work it's magic.
Do not cancel or close your browser. Just let WordPress do it's thing.
On completion, you will receive a status report with how the installation went.
If the WordPress report comes back successfull please proceed to the next step.
If you experienced problems you may need to do a manual upgrade.
See the WordPress support forum for more information
Step 8
Upgrade and reactivate plugins. A WordPress website may not view properly if the plugins are not activated even if the upgrade process went smoothly. There may be lines of code trying to pull in commands from the plugins that are not active and, therefore, cause error messages to display. After an upgrade appears to go without any issues, check the plugins section to make sure all the most recent versions of each plugin has been installed. After upgrading the plugins, reactivate them and check the website.
Sometimes, plugins become incompatible with newer versions of the WordPress software. If any error messages display after an upgrade procedure, try reactivating one plugin at a time to see which one might be causing the problem.”Check your website and make sure that everything looks fine and to be working.
Congratulations! You have just upgraded to the latest version of WordPress. If you received an error message whilst trying to upgrade, or your blog is experiencing problems, please see the WordPress forum.