Rub it down liberally with mineral spirits to get the black grime off, harder and more liberally where it is darkest.
Let it dry well in the sun and make sure the MS are well evaporated.
Put a coat of BLO on it, slop it on well and let it sit for 1/2 hour. After the 1/2 hour wipe off the excess BLO and let it sit for 24 hours. Repeat to taste 4 times or so and you will have a very nice looking rifle.
For mild cleaning I don't recommend anything but Mineral spirits.