Are you planning on doing this yourself or having a gunsmith do it?
It’d be cheaper to sell the one you’ve got and buy a better one to begin with. Granted, it’d still be in 8MM.
Basically, you need to remove the old barrel. You’ll probably want a barrel vise and wrench for that, and you’ll need those later anyway.
Then you’ll need a new barrel with the correct threads, and of course chambered for .308.
You’ll need to fit the barrel to the action - which will require the above vise and wrench. Plus you’ll need headspace gauges, and most likely a lathe to adjust your headspace.
You’ll need to fit the sights. You might need to turn down the barrel to fit the sights and/or to fit the existing stock and hardware. You might also need to shorten the barrel and crown it. You’ll need to blue or otherwise finish the barrel.
You might need to block off the magazine well for the slightly shorter round, though maybe not.
It’s your rifle, of course - but IMHO the trouble and/or expense isn’t worth it.