Changing out the barrel on a lever action rifle is a standard gunsmithing process well within the capability of a careful workman using common tools.
The relatively small barrel shank diameter and length of the Marlin 336/M1894/M1895 actions makes this relatively easy. The flat receiver is easy to hold using two hardwood boads or thick aluminum plates using a large "C" clamp. Avoid scratching the bluing with hard metal clamps against the gun.
You need to make up some barrel blocks from dense hardwood (oak, maple, hickory, etc) or better yet, aluminum. Chisel hemispherical grooves to hold the barrel over the chamber. You can use a large machinist's vise to hold the barrel next to the receiver using the barrel blocks. Tighten that vise until your eyes bug out!
Strip the action of all internal/external parts. With the action held and clamped securely close to the barrel shank, unscrew the old barrel. Usually a sharp "bump" with a mallet will break the barrel loose easier than slow, steady pressure.
The replacement barrel simply screws into place and should index correctly (front & rear sights aligned vertically, extractor cut aligned with extractor). If the barrel was correctly chambered, a factory cartridge case (bullet and powder removed, please!) will headspace correctly. Most Numrich replacement barrels should index and headspace correctly on the first try. factory original barrels are even better. They will almost always index correctly.
IF the barrel does not index correctly (needs to turn in more), then you have to hand fit the barrel shoulder to the receiver by filing or turning on a lathe. If the barrel turns in too far, you need to either peen the barrel shoulder to give it more "crush" or make up a spacer washer.
Checking heaspace on lever actions is simple too. Cut some 0.005" or 0.006" cartridge head sized discs from feeler gage leaves and use grease to adhere to a factory cartridge case. The action should barely close with 0.006" headspace. Anything more than that is excessive.