thank you for your question.
The easy way to register is to go through our website (www.a-kasser.dk). You can compare price and read about each a-kasse.
By cliking on link or A-kasse logo you will come to the particulary A-kasse website and in most cases directly to their online form, where you can sign up for membership.
All A-kasser has today online sign up. You fill out your details and receive confirmation on email. You will be member from the day you apply.
Please tell the A-kasse that you have been member in Sweden. I think you can transfer this member-period to the danish A-kasse, which will be good for you if you become unemployed during the next year.