The Bloch-state velocity is given by the first derivative of the electron band energy, E(k), with respect to the electron quasimomentum, k. If you want to calculate the Fermi velocity of graphene, for example, this velocity is then defined as the Bloch-state velocity calculated at the Dirac (conical) point of the graphene band structure, see
http://docs.quantumwise.com/manuals/Types/calculateVelocity/calculateVelocity.html.
Another example is a free-electron gas or any material that can be described with the free-electron gas model. The Fermi velocity can then be seen as the Bloch-state velocity calculated as the first derivative of E(k) with respect to k at the Fermi momentum, k=k_F, which is related to the highest occupied electron states, i.e., the states on the Fermi surface given by E(k_F)=E_F, where E_F is the Fermi energy.
I would suggest reading some basic Solid Physics textbook for a better understanding of this issue, e.g., Ashcroft & Mermin: Solid State Physics.
