Download the latest version directly from the developer's web site (typically the 64bit version):
https://www.chiark.greenend.org.uk/~sgtatham/putty/latest.html

Once downloaded, go ahead and install putty.

Click the Next button to continue.

Leave the install directory at the default and then click the Next button to continue.

If you want an icon installed on the desktop, click the red X beside the Add shortcut to PuTTY on the Desktop and change to install.
Click the Install button to continue.

You can remove the check mark for the View README file option and then click the Finish button to complete the install.