Quite straightforward. Just call BA in Sweden using the number on their website, make your booking, get on flight. Your booking will probably be handled by a call centre in Germany, but you need to call the Swedish number in order to get the Swedish price.

I only had one problem: my bank decided that the ticket value was over their floor limit, so they wanted to talk to me for a security check. Unfortunately the BA call centre's payment desk did not handle this properly (ie they just told me I was out of credit, which is wrong), so I had go to the counter in ARN in person on departure. Then when I got there, the counter agent had the wrong phone number to call their bank for the security check. This took 40 mins to sort, but was eventually fixed. BA(Finnair) were courteous and apologetic throughout.

Paying on Amex makes this problem go away, as I discovered with my next ticket.