Swedish cities are a nightmare for parking with restrictions on the length of stay and high charges.
Most roadside parking is paid for at ticket machines and you must display your ticket. There are often short periods for parking meaning that it's often inconvenient or expensive. To save the inconvenience, use a parking garage which is more expensive but you can stay longer. Parking is generally free on a Sunday in the cities.
No parking areas are signified by a blue sign with a red ring and red diagonal line across it. Parking there or outstaying your ticket duration can be monitored by the police or wardens in some cities. You'll get a ticket attached to your car or, if causing an obstruction, you may be towed away.
The European blue badge scheme isn't officially recognised in Sweden but it sometimes helps to show it if you're trying to get a more easily accessible spot. It won't allow you to park for free though! We recommend that you check local regulations before making assumptions.