Since there is no atmosphere in space, the typical control surfaces such as the aileron, rudder, or elevator, used on an airplane would serve no purpose. All spacecraft use what is called an Attitude Control System(ACS) or a Reaction Control System(RCS) to control the attitude of the spacecraft during powered flight and small changes in attitude, and linear or rotational motion on orbit. In other words if a spacecraft had to make a small adjustment in position or attitude, of either a pure translational motion, a pure rotational motion, or a combined motion, it would use the ACS/RCS to do so.
The ACS/RCS consists of several small rocket or gas thrusters uniquely located on the outside of the spacecraft plus the necessary fuel tanks, plumbing, valves, and controls. For example, the Space Shuttle RCS has 38 bipropellant primary thrusters and six vernier thrusters to provide attitude control and three axis translation during the orbit insertion, on-orbit, and reentry phases of flight. The RCS takes over control of the spacecraft above 70,000 feet altitude.
There are many different ways to arrange the thrusters to protect against the failure of any thruster so it would be too difficult to describe their locations and their functions here. There might be 12 thrusters located at each end of the spacecraft, four firing parallel to the X axis, four firing parallel to the Y axis, and four firing parallel to the Z axis, and they would be fired in pairs, to initiate pure translation, pure rotation, or combined translation and rotation. Sometimes there are more thrusters located around the center of gravity of the spacecraft.
The RCS would also be used to make small adjustments in position such as those required during the docking of one spacecraft to another. For larger changes or adjustments in orbital velocity, a much larger rocket engine would usually be used. On the Space Shuttle for instance they have what is called an Orbital Maneuvering
System to provide the thrust for orbit insertion, orbit circularization, orbit transfer, rendevouz and deorbit. There are two of these engines on the rear of the Shuttle and each provides 26,700 pounds of thrust. They are designed for 100 missions, and capable of sustaining 1000 starts and 15 hours of cumulative firing.
There are excellant books available on spacecraft design, history, missions, etc. in your public library I am sure. An excellant, very detailed book on the Space Shuttle is the reference cited below. NASA publishes many good references on spacecraft also.
I hope this has given you some idea how a spacecraft moves in space. I am sure that if you are interested in any more details, you can go to your library and find many good books that discuss spacecraft configurations and all the operating systems in a spacecraft. If you can't find any, let me know and I will look up some sources from my references or send you some additional information.
Ref: Rockwell International Space Shuttle by Dennis R. Jenkins, Aerofax, Inc., PO Box 200006, Arlington, Texas 76006, Phone 214-647-1105.