Tools you'll need:
NifSkope with Skyrim ini (or use Amorilia's, but may currently cause issues - thanks throttlekitty).
MaxTools 3.7.1 The forum post for this has unfortunately recently been merged and previously mentioned links are broken. This may change again soon, so I don't guarantee this link will work.
3ds Max (obviously) - I'm using 2014 x64
Importing the mesh you wish to change
First find your mesh you want to edit. You'll need to extract the nif.
Make sure you have the required skeleton nif file extracted to the same directory. If you're unsure, import attempts will produce an error telling you which skeleton you need.
In 3ds Max, import your mesh with the following settings:
Make your changes to your mesh.
It's your responsibility to ensure changes you make are valid: ensure the Skin has correct bone assignments and your UVW maps are good.
Export with the following settings:
Ensure Generate Strips is off. We need NiTriShapeData, not NiTriStripsData.
Remove Extra Bones shouldn't be necessary if you correctly checked Remove Unused Bones on import.
Save your nif and put it into the correct data folder in your Skyrim directory so the game uses it. You should now be done! Have a test and see if everything worked ok.
I hope this helps. I really cannot provide too much support for this, because even I don't fully understand it. But I hope my process, which I've found to work for me, will work for you too. And I apologise in advance if everyone finds that the method doesn't help when you actually do some serious modifications to your meshes. I haven't done so yet, so I can't guarantee it'll work right! But I hope the concepts will be a good base to work from.
Good luck and happy modding