The best way to do this job is to remove the door-trim from the inside of the house. HOWEVER, if you're not comfortable w/this, you may have a 2nd option.
With the 1st option, you can then stuff a foam-type based insulation in between the rough opening (the space you see.) Go to a local Home Center and tell them what you want to do. They'll help you from there. I'll spare you any details on how to remove or re-install the trim as I'll assume that if you go this route, you're comfortable with both ends of this method. As for the 2nd method, there is expandable foam. BUT, you have to be careful here! There is highly expandable foam and so-so expandable foam. Again, go to the local Home Center and tell them that you're insulating the door WITH the TRIM IN PLACE. And tell them you want the NOT-SO-HIGHLY-EXPANDABLE FOAM. It comes in a spray can with a fine tube for insertion into the cavity. Read the directions BEFORE you leave the store! Make sure it's OK for what you want to do (despite what the Customer Attendent tells you.)
At worst, find someone who is 'handy' and buy them some pizza and beer to help you do it via the 1st method. My best to ya and hope this helps.