Can I use OpenVPN with a single secret password instead of a keys set?

I am looking forward to create an as-simple-as-possible OpenVPN set-up.

I would like to use a single password to secure the communication instead of a set of key files.

How can I set it up this way?

Yes, OpenVPN calls this the "static key" setup:

http://openvpn.net/index.php/open-source/documentation/miscellaneous/78-static-key-mini-howto.html

Note the listed disadvantages:

• Limited scalability -- one client, one server
• Lack of perfect forward secrecy -- key compromise results in total disclosure of previous sessions
• Secret key must exist in plaintext form on each VPN peer
• Secret key must be exchanged using a pre-existing secure channel

To use password authntification from file, you should use this directives in server configuration file:

• client-cert-not-required to allow authentification with user/password only
• username-as-common-name to get common name from username, because it can't be taken from certificate
• script-security 2 to allow calling external scripts
• auth-user-pass-verify <script> <method> to force server ask for user/password. <script> is executable file used to check user/password pair. <method> is on of "via-env" and "via-file". Read manual about auth-user-pass-verify directive for details

You should write script by yourself.