The model class contains the bone/skeleton information you need.
You would have to draw each mesh separately. Instead of myModel.Draw(…)
you need to iterate through the Mesh parts and apply the rotation on the effect.
See this sample: Simple Animation · SimonDarksideJ/XNAGameStudio Wiki · GitHub
This might get slow for many models and/or ormodels with many meshparts. An alternative would be to use the SkinnedEffect, (see willmotil answer) and assign a single weight per bone/Meshpart.
You need a custom importer for that. That sample added this feature in the Skinning sample.
I also added this feature in my Animation importer Import Bone names by nkast · Pull Request #1 · tainicom/Aether.Extras · GitHub,
I guess you can just use that importer even if your model doesnt contain any animation, just use it as a regular Model
and the bone names -hopefully- will be there.