There are lots of parking places along the main street, so it shouldn't be a problem to find a place for your car. We were at the car-park "Langer Kamp", where only one part is free. For the left part you'll have to pay, but it's free on Sunday. It's the first car-park that you'll pass when coming from direction Lüdenscheid, at the main street and the street to the castle. From there it's a few minutes walk to the castle, but the street is not steep, and you'll also pass the Drahtmuseum.
If you don't feel like walking up to the castle, you can take the bus. It's a little bus that shuttles between the parking "Langer Kamp" and the castle. It drives daily, as needed.
The bus to the castle costs 0,90 € for adults and 0,50 € for children.
I strongly recommend that you explore the town on foot. Don’t just explore the castle side of the town but also cross the Lenne river and go uphill a bit. From the roof of a parking lot you get a nice view on the town and the castle.
This green bus from line no. 4 takes you up to the castle via the Drahtmuseum. It starts right on the big Bungern carpark in the center of town. They run not very often and only on demand. Please check the times carefully and have the castle cashier call for you when you want to go downtown again.
You can reach Altena by regional train from Hagen or Siegen. Best check the DB website. The train station isn’t too appealing but there is a kiosk/shop.