You build a team of four Desert Rangers (or take the default four) and set out from Ranger HQ to see how life in the Wasteland is going, and try to help rebuild civilization. Your characters don't have backstories. They're Desert Rangers, and you can fill in whatever imagination you want. There are tons of skills available, some of which are invaluable for at least one party member to have (percpetion, climb, lockpick), some that are good for all party members to have (various combat skills, swim), and many that are quirky and have only one or two uses throughout the game, but seem really cool and contribute a lot to how you view your character (sleight of hand, forgery, metallurgy, beauracracy, alarm disarm, bomb disarm, safecrack, knife throwing, acrobat, cryptography, toaster repair, helicopter pilot, clone tech). Some of those aren't available at creation and are only found at special libraries for characters with INT above starting level.
The first part of the game, about 20%, you deal with the "small folk." You encounter nomads, farmers, kids, and savages, and help them all fix their equipment or defeat their evils.
The second part of the game, about 50% of it, takes you through three towns/cities, each larger than the last. In Quartz, you encounter gangbangers, bar patrons, and politicans, and try to help them sort out their difficulties for great justice and progress. In Needles, you encounter monsters, mutants, cops, drunks, murderers, and cultists. You try to help them solve a murder mystery and defeat a psycho cult hellbent on a second apocalypse, and also start learning your first clues about the real story of the game. In Las Vegas, you take sides in a mafia war between two casino owners. You are also directed towards the real conflict: the increase in maniacal robots invading and attacking the city. You travel through the sewers beneath a church to reconstruct a helpful AI robot who opens up the final act for you.
Along the way thus far, you've encountered numerous NPCs that can be "hired," up to a party size of seven. NPCs are sometimes other Desert Rangers that were lost and had been long given up for dead, or gang members looking for something better to do, robots or humans who want to enlist you in their cause against the AI, or just regular people that need to be rescued and escorted to safety but will stick with you as long as you ask them to.
The final part of the game, about 30%, are the military and research facilities. The Guardian's Citadel, Darwin Base, Sleeper One, and Base Cochise. Two of them are science facilities that you mostly explore and are totally engrossed into tests of your char skills and puzzle-solving abilities (Darwin and Sleeper), and two of them you mostly assault head-on (Citadel and Cochise), fighting psychotic monks and killer androids and navigating mechanical traps. In the end, you defeat the evil AI at Cochise who was creating a robot army to destroy humanity.
At which point you get 10 attribute points (the equivalent of gaining five levels at once) and can continue exploring the game world forever, or you can keep your characters but reset some or all of the game world, or you can do a full reset (as fans did dozens of times) and start again with a whole new party.