Restoring worn down steps
Keep it Easy
If you're not looking for a specific finish, and just want something shiny and better than what's there now, and given it's the attic stairs and not your Grand Entrance:  I recommend you start with an easy approach.

Sand the stairs down with an orbital sander.  Go for 80/20 approach, stop sanding when it looks pretty good. That will take about a day. Don't spend another week making it 99%.
Apply two coats of tinted water-based polyurethane.  That's another day but mostly just waiting.

Very little effort, very little money, and it'll look pretty nice.   Then you can spend a year perusing woodworking sites, watching youtube videos and historical renovation sites to see if there's something you like better.