Not very.
The border between Sweden and Norway was (and is) 1 630km long and runs through some of Europe's densest forest most desolate mountain regions. While the border crossings were tightly controlled on both sides, it was possible to cross back and forth, both legally with the permission of the Swedish and German occupation authorities and illegally. People in the border regions had extensive contacts in both countries and often knew the terrain on both sides of the border from hunting, berry-picking and trecking. These men and women served as "border pilots", guiding individuals and groups across the border - from both sides - on small paths unwatched or rarely patrolled by the military forces on either side due to their remote locations. At times this was unpaid work, but as the US entered the war, the Norwegian legation (embassy) in Sweden gained more resources to pay border pilots for their work and the risks they took. Towards the end of the war, being a border pilot could make you a decent full-time living.
The Norwegian resistance periodically moved across the border and back to avoid the Germans when they got too close. The Norwegian embassy in Sweden, which expanded from 4 employees 1940 to about 1 100 1945, becoming an important centre to coordinate intelligence and MILORG (resistance) operations. Swedish authorites often looked the other way when known resistance fighters turned up at the legation to disappear again.
Roughly 70 000 Norwegian refugees crossed into Sweden during the war, most of them finding jobs in the forestry industry (as the lack of international trade made Sweden dependent on German coal and charcoal and firewood had to pick up some of the slack) and around 15 000 were eventually recruited into the so-called "Police" brigades (in reality soldiers trained and equipped like regular Swedish infantry) intended to help the Norwegian government restore order after the German occupation and deal with any remaining resistance, especially from the collaborators and the Hird, the armed wing of the Norwegian nazi party Nasjonal Samling.
The "Norwegian art club" was a cooperative project where MILORG, the Norwegian legation (embassy) and the Swedish military intelligence traded secrets, information and services, which included Swedish military intelligence smuggling British and American arms flown or transported by motor gunboat over the North Sea (with ball bearings as return cargo) to the Norwegian resistance - interestingly, the Swedish police attempted to watch and at time arrest members of the project as they were illegal aliens and/or spies, and turned the information over to the military intelligence, unaware that they were already involved in the project.
As the war progressed, more and more "couriers" to carry information, arms, equipment and other things were recruited, and the traffic across the border was quite frequent. The "Norwegian art club" delivered a full printing press, in pieces carried on the backs of men through the forests, to the Norwegian resistance to print anti-German propaganda.
On the other side, the majority of the roughly 160 Swedish SS volunteers crossed the border from Sweden, often legally, to Norway to sign up in Oslo. A few adventurers (or mentally problematic people) also crossed but were rejected, often spent a few days or weeks in a cell and were then deported back to Sweden.
There are persistent but unconfirmed rumours of Swedish jägare patrols entering Norway in accordance with the Swedish "free war" doctrine, to scout potential ambushes, German fortifications, infrastructure to raid and sabotage in case of war between Sweden and Germany.