Upgrading from a previous version of Tasks (2.x)
Just un-zip the new version and put it on your web server.
You will need to set your database settings in database.inc.php, then you are ready to go.
In version 2.6, the format of the database.inc.php changed so you will need to re-enter your settings if you are upgrading from a version prior to 2.6.
If you are upgrading from version 2.6 or later, you can keep your old database.inc.php file (don't overwrite it) instead of having to re-enter your settings if you like.
Log out of Tasks if you are still logged in, then log in again. If you are not using built-in authentication, go into your Server Settings and turn it on so that you can log out (you can turn it off again after you upgrade).
If the new version requires you need to run an upgrade script, you will be taken to the installer and walked through the necessary steps.
Upgrading from Tasks Jr. or Tasks 1.x
If you did not change the database table name from the default when you installed Tasks 1.x (left it as 'tasks'), you'll want to set your $table_prefix in database.inc.php to 'nothing' like this:
$table_prefix = "";
If you used a different database table name, you'll want to rename your database table or create a new copy of your table and name it 't2_tasks' (and use the default 't2_' table prefix).