I have an email address on my own domain that's forwarded to a Gmail address, so I can manage my email on Gmail. Lately I'm having problems with my email being marked as spam, so as one of the measures I'm taking to prevent this from happening again, I want to add DKIM authentication.
I came across this page: https://support.google.com/a/answer/174124?hl=en&ref_topic=2752442 which explains how to use DKIM when you're using Gmail on Google Apps. I use Gmail, but not on Google Apps.
Is it possible for me to send messages with DKIM and if so, how?
No, it's not possible to use DKIM with Gmail. But if you want to improve your spam-status, you should use SPF records. Add the following as a TXT record in your DNS settings:
v=spf1 include:_spf.google.com ~all