In PuTTY 0.78, the ‘Private key file for authentication’ control, where you specify a .PPK file for SSH public key authentication, moved to a new ‘Credentials’ panel in the configuration dialog. You can find this by opening the ‘SSH’ category in the tree view on the left, then opening the ‘Auth’ subcategory under that, then clicking on ‘Credentials’. On this page you'll find the ‘Browse...’ button you need to select a .PPK file for authentication, as described in section 4.22.1.
(This control had previously been on the ‘Auth’ panel since public key authentication was first released in 2002, so many online how-to guides still describe it there. The configuration controls were reorganised to make room for features added in 0.78, such as OpenSSH certificates.)