Basically, take it down the line of possibles...one at a time, until you find the answer.
First is pretty standard, check the torque on all screws, nuts & bolts, & make sure nothing wiggles at all.
Next, put it in a Gun Vise or other securing mechanism to determine whether it's ammo or the rifle itself.
You won't get .30-06 Bolt-Gun precision out of it...but you should get decent groups from 3"-6" @100 yds with open sights if you are a halfway decent shot. Less depending on how good you are and how well it's set up.
If it's got a scope, have it checked. Rings, mount, etc as well. I know a fair amount of folks that couldn't figure out the Locking Adjuster system on one type of scope, and would break them by not unlocking the adjusters before trying to turn the knobs...which led to all sorts of no-pattern problems.
For accurizing tips, try this board...
336
The 336W & 30AW are the same, 336W is just the newer model designation.
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the 30AW is the Wally world equivalent to the 336W with a Birch stock, no pistol grip cap, and no white spacer in the butt plate. If it has checkering, it's the pressed checkering, not carved checkering.
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Serial number dating works the same as the 336.
Here's real good examples of how to start out with a New lever-action
300 yrd. 30-30?!! New 336W 30-30, Cabela's Levergun scope, LE ammo Review Making This Dog Hunt: taming a see-thru mount on my 336
With testing, all things are found
With more info, we can help you figure out the problem...or hopefully you are near one of the guru's and can be helped at your local range