How do rockets spin and pitch at the same time How do rockets spin and pitch at the same time? Thrust vectoring using a gimbal which basically just always faces down, so that shouldn't cause it to pitch. Since the rocket is spinning, using the fins to pitch wouldn't work unless they only activated for a portion of each rotation. Using the fins in such a manner seems like it would be extremely difficult and prone to malfunction.
EDIT: I'm specifically talking about the rockets we use today. They launch upright, and generally arc before they release their payload, while spinning along their vertical axis. The Saturn V is one example of this.
 A: There are multiple methods of control, and they depend on whether the craft is still in the atmosphere or in vacuum, and if you only have a single engine on centerline, or if you have multiple engines.  
Any method that provides side thrust can provide roll control as long as it is not on the centerline.  Multiple engines, side thrusters, and movable fins can all work. 

In the case of the shuttle, the main engines were away from the centerline and had plenty of authority to roll the craft in flight by gimballing.  The Saturn V first stage had four outboard engines that could gimbal to control roll, pitch, and yaw.  The Saturn I (which had only one main engine on centerline) had an auxiliary propulsion system (APS), which were smaller thrusters.  These provided roll control in flight (among other functions).

A: First of all your question uses the term 'spin' which in rocket science implies a continuous angular velocity along a particular axis of the spacecraft. Spin is often used to maintain a constant angular momentum and stabilize a spacecraft during flight to keep it from tumbling. After a spacecraft is put into spin, it no longer requires gimballed rocket controls to maintain stable pointing. But in a spin state some form of nutation control is required. Spinning may continue to be used throughout the mission, but some spacecraft missions require de-spinning after they have reached their station, for example a planetary orbit where a satellite is required to point an antenna nadir. After de-spinning, different systems of sensors and actuators may take over to stabilize the spacecraft including propulsion mechanisms, reaction wheels, magnetic torquers, etc. 
But in either case during the spinning phase of flight either pitch or yaw motions can be accomplished using out-board thrusters located off the center line of the main thrusters. The outboard thrusters, through appropriate timing can be used both to keep nutation in check and re-direct the flight path.
But maybe you meant 'roll' rather than spin. Roll motion is rotation about the axis pointing in the direction of flight and is usually a term used to describe a shorter maneuver rather than a continuous spin rate. Rolling and pitching of a booster simultaneously can be done using multiple gimballed main thrusters, or if there is only one main thruster, using outboard thrusters.
