Read the "What If..?" line, and understand its basic place in Marvel's mythology. "What If...?" comics explore alternate possibilities that don't follow the canonical Marvel timeline. The comics were originally conceived as a place to play with intriguing notions, such as a villain killing a hero and taking over the world, or a hero deciding to become a bad guy instead of a good guy. Spider-Girl originally appeared in "What If," Volume 2 #105: positing an alternate future for her father, Spider-Man. She proved so popular that Marvel soon developed an entire comic book series around her set in that alternate future.
Familiarize yourself with Spider-Man's mythology. Spider-Girl possesses many of the same powers as her father -- such as the ability to stick to walls and a "spider sense" that warns her of immediate danger. More importantly, much of her personal mythology is pulled from the Spider-Man comics. For example, her real name is May Parker (or "Mayday" to her friends.) She was named after Peter's beloved Aunt May. She also faces many of Spider-Man's classic foes, such as Doctor Octopus and Venom. Knowledge of Spider-Man will help you grasp her adventures more readily.
Study the specifics of the alternate universe that Spider-Girl occupies. It's officially referred to as MC2, a "possible future" for the Marvel Universe approximately 15 years after the current Marvel timeline. It contains some key differences from the canonical timeline; for example, the Fantastic Four are now the Fantastic Five, and the world's heroes include Wild Thing, the daughter of Wolverine and Elektra. If you know who these other characters are -- and more importantly, the way they diverge from the canonical timeline -- the storylines become easier to follow.
Read the Spider-Girl comics from the beginning. After the "What If..." comic that introduces her, she appears in the "Spider-Girl" and "The Amazing Spider-Girl" comics. Many of these are out of print, but Marvel has collected them into trade paperbacks which you can purchase at Amazon.com or your local comic book store. Reading them from the beginning will let you appreciate the various story arcs without becoming lost.