The LEGO building system can let you assemble anything from a simple rocket to NASA's space shuttle with rocket boosters and a launching rig. The only limitation is your imagination; you can choose how futuristic or modern this rocket is. There are just a few simple things to keep in mind. You'll find your own space program assembled and ready for lift-off soon.
Build the fuselage of the rocket. This is the body of the rocket and is usually long and thin. The bulk of the fuselage on a real rocket contains the fuel mixture needed to lift off. Depending on the diameter of your rocket, you can use any width of rounded parts. To reinforce the fuselage, some parts will accommodate a Technic rod in the middle. Make sure you use as many of the same part as you can acquire to make the body of the rocket.
Assemble the nose of the rocket. In modern rockets, this is where the pilot and equipment for the mission are housed. On smaller rockets, a simple cone will suffice. For larger models, build a capsule that can contain a payload: human, animal or simply scientific. Use hinge pieces to build a payload chamber door, if you are adding one.
Build the tail fin section. To stabilise the rocket while exiting Earth's atmosphere, many rockets have a system of fins along the bottom of the fuselage. The fins on a typical rocket aren't much wider than the radius of the rocket. On space shuttles, however, the fins form a wing on the bottom and a stabiliser, like that of an aeroplane, on the top.
Build the rocket nozzle. On a real rocket, this is where the fuel mixture burns and mixes with oxygen to create a burning explosion. The nozzle controls the explosion, propelling down to make the rocket fly. Single-stud cones at the bottom of a device make excellent adjuster nozzles; larger cones are ideal for larger boost nozzles.
See the NASA webpage under Resources for more information on rockets, including how rockets work and what real rockets look like.