This app was mentioned in 2 comments, with an average of 6.50 upvotes
Pretty easy. Best way is to walk to Sergels torg, where T-Centralen is (the central subway station). There you take the southbound green line towards Hagsätra or Högdalen. Globen is 6 stops away, the ride takes about 10 minutes.
(You can also take the blue line from Kungsträdgården to T-Centralen and switch to the green line but the walk is only 5-10 minutes).
I recommend using an app to plan your public transport trips for you, it is for all SL lines; buses, subway and local trains.