1. Take them entirely apart, even the bolt (762x54R.net has exploded views). Get rid of any commie cosmoline left in the receiver. Clean and re-lubricate with a good gun oil.
2. If you like the wood, refinish it with Tung Oil. Clean all of the old nasty varnish off, and put about 5 - 7 coats of Tung Oil, allowing a few hours between coats to dry. I did this with one of my M39's, and it looks great.
3. If you want to run it open sights (fine for an M44, and I've shot 300yd open sights with an M39), get the Mojo "peep" sights. No gunsmithing required. They mount and work perfectly. I think I paid $45 for mine, but that was about 2 years ago.
4. If you want a scope mount, STAY AWAY from the "bolt on" "no gunsmithing" type. Get a local gunsmith to drill and tap your receiver (painful I know on a classic like a Nagant), and you will have a MUCH more stable scope platform. In my humble opinion, unless you are left-eye dominant and right handed, STAY AWAY from the left-side Russian-style mounts.
5. Get yourself a good sling. Your Nagant may have come with one, but you'll be glad you got a good one.
6. If you are planning to reload 7.62x54R, go ahead and order the material (for example, from Midway USA) to "slug" your barrel. Nagant barrels do vary, and you want to measure the rifling land diameter. Mine slugged out at about .311, so I use 303 caliber bullets from Sierra and others.
Congrats on a great historical rifle.
Thank you very much.