Lesson #1: Set the Stage
Whether it's aliens, futuristic technology, or a post-apocalyptic setting, something about your sci-fi universe is going to be unfamiliar to the viewer, no matter how many times they've seen it in other films. Sometimes it works to be thrown into the action and figure things out as you go (see: Star Wars), but even then there's a certain amount of context that needs to be established. Oblivion takes the time to explain loads of backstory before the movie really begins, but the exposition is concise and effective—within the first five minutes, I had a firm grasp of the universe, these characters, and the life they lead, immersing me in the story before much of anything had happened. All too often I've seen movies devote too much screen time to introductions and backstory that are vital, but delay the start of the main plot (see: Harry Potter). Just as often I've seen movies that tell you nothing, possibly glossing over some critical backstory more than halfway through the film (see: Star Trek (2009)). Oblivion tells you everything you need to know up front, devoting the rest of its running time to telling the main story and further developing these characters you feel like you already know.
Lesson #2: Subvert Expectations
A hero lands in an empty field to repair a damaged drone that was shot down by scavengers. As the screenwriter, you should:
a) allow the hero to fix the drone, but be ambushed by scavengers on the way back
b) allow the hero to fix the drone, but have it malfunction and try to attack him
c) allow the hero to fix the drone, and go about his business
Most any other movie would've picked a) or b), but Oblivion frequently comes up with an option c). Murphy's Law is usually in constant effect elsewhere in the cinema world, because turncoat technology and overwhelming odds tend to make for better drama than when things go as planned. Oblivion uses this to great effect—every time something goes right, it builds greater tension for the things that go wrong. Veering away from the obvious while staying within the realm of reasonable possibility makes the story feel more authentic and less contrived, and it's easier to invest the audience in your story when they really don't know what will happen to the characters.
Even in the places where things do happen as you expect them to (a few minor deus-ex-machina moments come to mind), they're not overdramatized.
Lesson #3: Use Death Responsibly
From the noblest of heroes to the lowliest of Stormtroopers, people die in movies all the time. Death is often a climactic emotional gut-punch (see: Serenity) or an obligatory component of action sequences (see: Flash Gordon); all too infrequently do characters die as a natural consequence of choices and chance. Oblivion kills off its share of individuals, whether we know their names or not; the difference is that it would do the same regardless of whether an audience was watching.
Lesson #4: Always Keep One More Secret Up Your Sleeve
Oblivion is full of plot twists. Sometimes it's an unexpected revelation about the plot; sometimes it's the unexpected actions of the characters; sometimes it's a bona-fide out-of-the-blue surprise. Up until the very end, there's always something more for the viewer to discover about the characters and the universe. This also makes for a fresh experience re-watching the film, knowing now what you didn't know then.
Overall? I could stand to see more movies like Oblivion.