A more detailed history can be found in the timeline, but this guide will fill you in on the main points you need to know.
After their first encounter with the Goa'uld, the New Republic allied itself with a small planet called Earth which was knowledgeable about the Goa'uld and the Stargate system. Rogue Squadron was briefly based in Earth's Stargate Command, where they discovered the Goa'uld System Lord Sobek had allied himself with a lost Imperial fleet commanded nammed High Admiral Steele, and the two forces were pooling their resources to build a Super Star Destroyer and conquer the Unknown Regions.
Rogue Squadron soon established its own base, Farpoint, and began to amass a larger military force to take on this threat. The alliance was eventually believed smashed, and Sobek killed.
The story of Rogue Squadron's first few years is largely told in canon fics starting with 'Origins' and ending in 'Showdown'.
After a relatively quiet period involving run-ins with pirates, traitorous elements of New Republic Intelligence and other System Lords, Rogue Squadron discovered that Lord Sobek and High Admiral Steele's forces were once again working together. Unknown to them, Sobek had not perished, but inhabited Steele's body and taken control of both parties.
Rogue Squadron continued to fight this renewed threat, including one assault on an Imperial cloning facility churning out new soldiers for Sobek's army. During the battle an insane clone of an Imperial general calling himself Malphuus escaped into the galaxy and soon began involving the Goa'uld in his twisted schemes.
Malphuus managed to become second-in-command to the System Lord Khepri, who he tricked into allying himself with Rogue Squadron against Sobek. Both Sobek and Khepri were destroyed by this face-off, allowing Malphuus to step out of the shadows and take control of the Imperial fleet, Sobek's domain, and Khepri's domain.
While this threat looms over them, Rogue Squadron has been struggling against a third party made up of Imperial officers and Goa'uld who've seen through Malphuus' ploy.
This story continues to play out in official RPG scenarios.