PuTTY is a bit different: it's got no .ssh directory to read from, it brings its SSH client implementation with it. If you want to configure PuTTY to use SSH key authentication, you can just follow these steps.
Setting up your keys for PuTTY
Both if you own or not your own keys, you need another program to produce a file for PuTTY to read: PuTTYgen. When you run it, puttygen will let you import your private key and save it in a PuTTY-friendly format or, if you haven't got one, to generate your brand new key. If you prefer not being asked a password by TortoiseSVN again and again, you can just avoid protecting the key with a passphrase and store the key in a safe place. I'll repeat it: store the key in a safe place.
Once you've done with the process, you will have a ppk file you should better store in a safe place!
To tell PuTTY to use your key, just open it, go to Connection/SSH/Auth and browse for your key file in the Private key file for authentication... field. Now you can save your session and you're done.