I mean, as much as they are fantasy based on a fictionalized and biased novel based on the historical events, the Dynasty Warriors games are actually a pretty good intro to the period, and they almost always have an encyclopedia section with more accurate info. I definitely know way more names cause of those games than I could if I just learned it in a classroom.
So, to start, the Han Dynasty was falling apart, lots of civil war, lots of unhappy common folk, and then Zhang Jiao, a mystic who preached about 'The Way of Peace' and united a ton of unhappy peasants into the Yellow Turbans (or Yellow Scarves) which rebelled against the Han government. Though they were quashed by a coalition of notable and eventually notable figures, such as Cao Cao, Liu Bei, Sun Jian, Dong Zhuo, etc, it really expedited the collapse.
Bunch of Unics in high position of power abuse it, piss off the Yuan family (Yuan Shao and Yuan Shu), they (the unics) get killed off, but this lets Dong Zhuo make off with The Emperor and again, makes everything terrible, eventually leading to another major coalition formed by Cao Cao but lead by Yuan Shao to stop him. Again, bunch of notable figures unite, again Cao Cao, Liu Bei (though still not famous at all yet), Sun Jian (who did alot of heroic things during this but they often get attributed to Guan Yu instead), Yuan Shu, though they fail in actually stopping Dong Zhuo or saving the emperor, though Sun Jian finds the Seal of the Emperor which is important later.
Lu Bu eventually betrays Dong Zhuo, killing him, but he gets chased away by the rest of Dong Zhuo's forces lead by Guo Si so he goes and wanders for a bit, eventually causing some chaos and trouble for Liu Bei, Cao Cao and Yuan Shu.
During this time, Sun Jian dies and Sun Ce, his eldest son takes over, uses the Seal to get troops from Yuan Shu and to get Shu off his back, Yuan Shu proclaims he is Emperor, some consider it legitimate, some dont, but Sun Ce goes on to conquer a ton of South East China before dying and passing power to Sun Quan, his younger brother.
Meanwhile Cao Cao and Yuan Shao are fighting for control of the north, with Liu Bei caught in the middle (he is on Shao's side, but Guan Yu got stuck helping Cao Cao, but they unite and abandon both sides eventually). Cao Cao defeats Yuan Shao at Guan Du, major victory for him, Shao dies, and his forces either join Cao, or hide north with his 3 sons who Cao eventually destroys as well.
Liu Bei flees from Cao Cao who is chasing him down, eventually seeking an alliance with Sun Quan with the aid of his new strategist Zhuge Liang. This leads to the battle of Chi Bi, which the combined forces of Liu Bei and Sun Quan defeat Cao Cao despite Cao's greater naval forces, this is a major blow to him which lets Sun Quan expand and Liu Bei goes and takes over central China, though this ends up causing conflict with him and Sun.
Liu Bei eventually conqueres what was then western China, taking over his relatives lands Meanwhile Cao Cao is asserting control over northern and north-western China, and Sun Quan is dealing with his region. At this point, I forget the specific order of events, but Cao Cao eventually becomes 'King of Wei', Liu Bei takes over Han Zhong which emulates his ancestor and founder of the Han Dynasty, Liu Bang and he declares himself King.
Cao Cao dies, his son Cao Pi takes over, forces the Emperor that Cao Cao had been maintaining control of to abdicate, Cao Pi declares himself Emperor, so Liu Bei and Sun Quan also declare themselves Emperor, and this officially starts the 'Three Kingdoms' period proper.
From this point its a whole lot of stalemating. Ugh, forgot to mention the Battle of Fan Castle, where Wei and Wu united to stop Guan Yu in central China, resulting in his death, enraging Liu Bei and causing his alliance with Wu to fall apart, leading to a disasterous battle in Yi Ling, with Liu Bei dying shortly after, control of Shu going to his son Liu Shan, though much of the power was with Zhuge Liang. Shu and Wu would maintain an uneasy alliance for much of the rest of this time, but never really trusting eachother.
Shu and Wei would fight alot in the north, but neither getting much headway, eventually Zhuge Liang would pass, giving chancelorship to Jiang Wei, a controversial figure. Meanwhile, Liu Shan was being manipualted by a court unic, and this plus Jiang Wei's inability to invade Wei kept Shu from growing much.
After that, Cao Pi dies and his son Cao Rui takes over, he is terrible but then he dies and then rulership just changes from Cao to Cao while the Sima family slowly takes over. Alot of backdoor politics, betrayal and manipulation eventually leads to the Sima Family controlling much of Wei, they eventually defeat Shu, capture Liu Shan who surrenders, though Jiang Wei continues to cause minor conflicts, and a ton of poor leadership in Wu also leads to the Simas toppling Wu under Sima Zhao, with Zhao's son, Sima Yan becoming the first Emperor or Jin, ending the Three Kingdoms period.
This is just a summary, mostly from memory, so do not take my word for law, I skipped a bunch, probably neglected a ton of important stuff even for a summary, and got some things mixed up. But its something.