First you need Nifskope and a 3D Modelling program like Blender or 3DSMax (or Maya, or Hexagon or Milkshape etc.)
Then you load the NIF into Nifskope, and use File / Export / Export .OBJ.
OBJ is a file format any 3D-moddeling program can work with, it's a text file, so if need be you could even edit it by manually changing the vertex coordinates.
Load the .OBJ into your 3D-modelling program and edit it. (That's the hard part if you never used one, and the free Blender is even hard for those who have used other tools) When you're done save again as .OBJ.
Now load that NIF again into Nifskope, select the NiTriShape entry and import the .OBJ.
When everything is white and the new model didn't replace the old one you haven't selected a NiTriShape node.
When everything has the same color you might have forgotten to UV-map the modified model before exporting it.
Also check the Tangent spaces (Normals, Tangents and Binormals) under NiTriShapeData, you might to have to re-create them.
When you're done, save the NIF, and use the CK to add a new item, or save with the vanilla filename to replace the old one.