If you want to use your Putty generated private key (.ppk) in Linux with not only Putty, but other SSH or SFTP client (Terminal, Nautilus, GFTP, etc), you have to convert it to OpenSSH's private key format, because putty private key format (.ppk) is not compatible with OpenSSH.
First, install "putty-tools" package, if you did not install it yet, because it is included puttygen.
apt-get install putty-tools
Now, convert your .ppk to OpenSSH's key format:
puttygen /pass/to/my-putty-privatekey.ppk -O private-openssh -o
For example, if you use RSA authentication, your OpenSSH private key: /home/user/.ssh/id_rsa
Putty public key format is OK, copy it simply to /pass/to/my-openssh-key.pub
For example, if you use RSA authentication, your OpenSSH public key: /home/user/.ssh/id_rsa.pub
And of course, set the right permission to your private key file (chmod 600)