One thing I have found with g/s d/t 336's is that sometimes they are drilled to close to the shooters face and sometimes they have hidden shoddy workmanship under the mounts.
Mark the center of the action with a sharpie, then align your weaver base and clamp it to the gun with one of those plastic ratchet type cabinet clamps, and mark the exact center of each hole with a scratch awl lightly just so you can see it. Unclamp the base and make sure those light marks correspond with your careful measurments you took as well. (If not then start over) use a center punch to deepen each mark. You really don't need the base, but I like to visually see it as well as measure it.
This is a good time to just do a total break down of the gun so that you do NOT drill into anything unwanted and get shavings in bad places, that way you just have the action clamped and not an entire gun. Don't be afraid to use painters blue tape on places that might get some unwanted scuffs.
You WILL MOST DEFINATELY NEED A DRILL PRESS AND VICE, and you will need to make sure that the action and the drill bit are making a perfect 90 degree angle between the two. Level the base of the machine with shims or whatever if need be, because it is important that the bit be perfectly vertical if you have taken the time to put your level on top of your action to make sure it is level (right?!). Use some cutting oil and take your time. This is not that big a deal IMO.
I figure a grown man can make his own decisions in life. Anyway, its fun to be self reliant in a world where your rifle barrel says that if you discharge it someone may get hurt, and your child is in a car seat until they are in the sixth grade, and your coffee cup has a "Caution HOT" printed on it.
I think a smith wants about $20 a hole nowadays FYI (which is fairly reasonable but this may take them a while to get to knowing them the way I do

).
I have a couple of basic gunsmithing books that I am not next to right now, one of them is actually pretty good and a good reference, if you want their titles let me know.