thank you for your question.
what you should do first depending on what you do at the moment.
If you are studying you should apply for free membership. Se more: http://a-kasser.dk/students/.
If you are working you should also apply for (paid) membership, you must be member for at least one year before you are eligile
for unemployment benefits.
If you do not have work and is not yet member of A-kasse then you should contact Jobcenter to get "kontanthjælp".
Normally you should first consider register at the Jobcenter when you get unemployed.