Who are the main characters in October Sky?

The protagonist of the film is, of course, Homer Hickam, the teenage son of a coal miner who wants to pursue aeronautics, much to the dismay of his traditional father.

Homer’s father, John Hickam, serves as the primary antagonist of the film. He wants his sons to continue in the coal mining tradition, and he has a difficult time understanding Homer’s interests. He also thinks Homer is chasing a pipe dream, and he pressures his son to be more realistic.

On the other hand, Homer’s teacher Miss Riley encourages his intellectual curiosity and pursuit of rocket science. She serves as Homer’s coach, in a way, and always pushes him to act rationally while following his heart.

Homer is aided in his pursuit by several friends, but I wouldn’t consider them to be main characters. These three are the most important throughout the film since each functions in a key literary role.

Who helps the characters achieve their dream in October Sky, and how?

Oh, Homer's dream is quite grand, isn't it! There are many people who help along the way, most notably friends and teachers.

Homer is the one who desires to build the rocket first, but if it weren't for the help of Quentin Wilson, it probably never would have happened. He is the class nerd, but he sure knows a lot about science and helps Homer with the research. Roy and Sherman (Homer's friends) help to a lesser extent, but the teacher Miss Riley is of the utmost support, giving them a rocket science book that helps them figure out the trajectory of rockets. We also can't forget Ike Bykovsky who was a shop worker who was IMPERATIVE in giving the boys the supplies for their rocketry. (It is Ike's death in the mine that disillusions many of the boys and especially Homer.)  Even the principal, Mr. Turner, helps the boys by proving that the fire is NOT caused by the boys' rockets, but by a flare from the corresponding airfield! It is John and Mr. Bolden that use the shop to repair a nozzle stolen at the state science fair and help Homer (and friends) win! The boys name their highest rocket after Miss Riley who dies from cancer.

In conclusion, I should say that there is an irony that the mine that has trapped the boys in a life of despair is also the vehicle that allows them to succeed. Without the machinery in the mine shop, the rockets never would have soared!