I use an old tee shirt...

Dab it on and wipe the track down with a finger of tee shirt.   Wear gloves if you want and a little ventilation  is nice.  When the tee shirt gets too dirt start using a new section.  

I know some guys have cleaning cars and use it in there

I put it on a cloth...

I put some on a cloth and use my finger to wipe the inner railhead with the cloth.

I use Old T Shirt material too.

Gun Cleaning Swabs

I use disposable gun cleaning swabs, as recommended by Joe F. They’re like common cotton swabs, but with a longer stick and tougher, tighter weave ends.

I don’t like the idea of having solvent soaked rags around the shop, since my railroad shares space with a gas water heater for the home.

Centerline cars

I use one “wet” followed by one dry.  I also have a Trackman car which drags a pad of bright-boy-like material on the track, which I run in front of the CL cars.

Eco-friendly

I, also, use mineral spirits and basically use the same procedure as mentioned above. However, I would mention that mineral spirits are available, as eco-friendly, by Jasco Green. I buy mine in Lowe's, as well as bags of white t-shirt material. You could use old undershirts, however, I use my old ones for painting to protect my good clothing. Glenn

DUST MONKEYS

I use the Woodland Scenic Dust Monkeys to apply the Mineral Spirits.  Let the engine do the work, keeping my big hands away from tall of the delicate scenery.

https://woodlandscenics.woodlandscenics.com/show/item/TT4571

Good luck,

Mark