That is a difficult question, but here is a summery of the story.
This story is told by the Main male character of the series, Kyon, who acts as the Narrator for both the anime and the light novel.
Kyon enters his first year of high school, and at this point of his life he has dropped all those childhood fantasy's that we all had at one time or another. He no longer believes on things like Aliens, Time Travelers, Espers, Demons, etc etc. He is ready to live a normal high school life and have normal high school experiences.
That is until the day he met Suzumiya Haruhi...
This girl, who sat behind Kyon gave this introduction:
"If there are any Aliens, Time Travelers, Espers, or Sliders here please follow me! That is all."
This is where Kyon's life is thrown off the deep end of reality. Because he talks to Haruhi and gives her the idea to form a club to find the "mysteries" of the world. He is forced to join along with three other members: Yuki, Koizumi, and Mikuru.
These three people Kyon learns just happen to be a Alien, Esper, and Time Traveler (respectively)
But Kyon is further forced to learn that this girl, Suzumiya Haruhi is also not an ordinary girl. This girl who so wishes to meet and experiences mysteries things has the power to make whatever she wishes come true. She is in a sense God, but she doesnt realize it and the secret goal of the SOS Brigade (the club Haruhi makes) is to keep her from becoming bored and changing the world as well as keep her from knowing of her powers because of the danger that could pose.
The novel itself consists of 9 volumes, 5 of them are story lines that pretain to the main plot of the series while 4 volumes are a collection of short stories that happen inbetween or during events in the main plot that are significant.
Kyon goes through many different unbelievable situations that include:
Being sucked into a new world created by Haruhi (Volume 1)
Making a movie of Haruhi's that alters the world (Volume 2)
Being thrown into a world where Kyon has lost Haruhi and everyone has lost their memory except for his own (volume 4)
Completing missions with Mikuru to save the future (volume 7)
The true enemy starts to show its face and things begin to set in motion (volume 9)
Some of the short stories include:
Kyon traveling back in time 3 years
Kyon spending almost 600 years reliving his summer vacation
Being trapped by aliens in a mansion in a blizzard
Completing various tasks to save his own life as well as the lives of his fellow brigade members
and much much more....
Its a VERY good series, you should def check it out!