I have my personal digital signature on the special card and the according reader. How can I sign an email (sending it with gmail) with this signature? I am on the latest OSX and use Google Chrome (but can use Windows 7, if it is really required).
Gmail doesn't have built-in support for encrypting and signing the emails, so there are others options you could try:
Note: There is an ongoing project for a Chrome extension named "End-to-End" which provides encryption, decryption and digital signature. It is not open for general use yet.
Use add-ons for Google Chrome i.e. EnigmaGPG, Mymail-crypt etc.
You can use PGP (Pretty Good Privacy). It works on public-key cryptography. First you have to generate a public-private key pair via GPG. You can sign the messages manually and make it armoured to send (provided the recipient has your correspondent public key to decipher) or in Mac OS use the gpgtools which contains everything to secure your communication.
There are email clients like Thunderbird which has the support for PGP via enigmail or openPGP.
Visit this site for the "End-to-End Chrome" extension.