The flight from ORD arrives at gate F58 or F62, on the 4th floor. Take the elevator or escalator down to 2nd floor, where immigration is. After immigration, you'll be in the baggage claim hall.

If you want to visit the lounge on arrival, you'll need to clear security. The nearest security is right after immigration, just 20 steps straight ahead after the passport control. The lounge is located on the 4th floor next to gate 1. Follow signs to gate 1. But beware that going through security and to the lounge could take up to 10 minutes. After visiting the lounge, return to gate 1 and go down the escalator. This will bring you back to the baggage claim hall.

After exiting customs, turn left, and 30 meters on you'll reach the escalators that will bring you down to Arlanda North train station, whence the Arlanda Express train departs. Buy tickets in the machines in the station, as there's a surcharge when buying on board.

(If you want to leave your bag at ARN, you'll need to turn right after customs. After the 7-Eleven, take the first escalator down on the left. That will bring you to a place with lockers and manned storage by Bagport. After leaving your bag, go back up again, turn left and take the escalator right in front of you down to the Arlanda North station.)

The train ride should take 20 minutes. If you go straight to the train, and if you're a quick walker, you should be in the city within 40-60 minutes after docking at the gate.

When you return from the city, make sure to get off at the last stop, Arlanda North. Take the escalator in front of the train (the same escalator where you descended in the morning), but continue to the departure hall. (This is assuming that you didn't leave the bag at the airport. If you did, take the other escalator, at the end of the train.) Turn right, and you'll be at security.

The security lines at this specific checkpoint are usually quite short around noon. After security, you have to go through a tax free store to get into the transit hall. If there's still time to visit the lounge, it's the one at gate 1. But beware that you have to walk back to the exit at the tax free store again to reach your flight. The SK flight to SVO departs from a gate in the F pier.