Activate only when an effect is activated that would destroy 2 or more cards you control. Negate the effect and destroy that card. Then, you can Special Summon 1 "Stardust Dragon" from your Extra Deck.
This Normal Trap Card responds to an effect that would destroy at least 2 Cards on your side on your side of the Field (more about this in a minute). It cannot be activated during the Damage Step. It negates the destructive effect and destroys the Card that performs it, and additionally, if it succeeds in destroying that Card, you can Special Summon a Stardust Dragon. Since its an effect that may perform a Special Summon, Royal Oppression's effect can be chained to Starlight Road (even if it is impossible to Special Summon for any reason). Starlight Road must be chained directly to the effect that you want to negate.
The first thing people get mixed up is what it means that an effect would destroy 2 or more Cards on a side of the Field. Here, you need a principle of certainty. That is to say, how sure are you (or rather, the Game State) that 2 Cards on that side of the Field are going to be destroyed? This is not as hard as the examples suggest. The easiest way to do this is to ignore every other Card that you may think of, and assume that Starlight Road will resolve properly. If it were to resolve properly, how many Cards would be destroyed and where? The answer lies there. Here are some examples for you to get the idea:
1) My opponent activates Torrential Tribute, while he has 3 set S/T Cards, and I control 2 monsters. I wish to activate Starlight Road. I ignore that my opponent has an Enemy Controller to take control of one of my monsters, or a Bottomless Trap Hole to get rid of my second monster. If none of those possiblities existed, how many monsters would Torrential Tribute destroy? My two monsters. And so, I can activate Starlight Road.
2) My opponent controls Yubel - Terror Incarnate, while I control 2 monsters and an active Skill Drain. Terror Incarnate's mandatory effect activates, and I wish to activate Starlight Road. I proceed to ignore Skill Drain. If it didn't exist, would Terror Incarnate destroy my two monsters? The answer is yes, so I can activate Starlight Road, even if Skill Drain would actually negate Terror Incarnate's effect and my monsters would remain intact anyway.
3) My opponent activates Saber Slash while he controls 3 X-Saber monsters, and I control 3 face-up monsters. I wish to activate Starlight Road. Even if I ignored every other Card, I cannot be certain that Saber Slash will destroy 2 Cards on my side of the Field, because my opponent has the possibility of destroying his own X-Saber monsters. I can suppose it will destroy 3 Cards, but I cannot know which three Cards. Note that this is true even while ignoring outside Cards. You never consider "what ifs" other than the effect itself that you want to negate. Otherwise, reffer to example #1.
4) My opponent activates Detonate. Ignoring every outside Card, I can determine that my opponent is allowed to destroy a number of my Cards. Let's say, my opponent has 3 Kuribohs, so he can destroy 3 Cards on my side of the Field. However, my opponent can choose a number up to 3, and so, I cannot determine if my opponent will choose to destroy a single Card I control. Not even if I ignored outside Cards. And so, I cnanot activate Starlight Road.
5) My opponent Tribute Summons Mobius the Frost Monarch and targets 2 Cards in my S/T Zone. I can activate Starlight Road, because ignoring outside Cards, Mobius has targeted 2 Cards on my side of the Field and aims to destroy it. This shows that the term "up to" doesn't equal a failed Starlight Road.
Once you grasp that concept, any scenario is much simplier than merely guessing. It's all reduced to interpretating which Cards can the effect destroy, how many, and where.
Other than that, there's the Special Summoning effect. The first thing to notice is that you must succeed in destroying the Card that generates the destructive effect. If something like Mystical Space Typhoon is chained to destroy that very Card, you are not allowed to Special Summon Stardust Dragon. Another important note is that this Special Summon is NOT a Synchro Summon, so the Stardust Dragon cannot be Special Summoned from the Graveyard or Removed from Play Zone by Card Effects (not even its own). This improper Special Summon cannot be "ignored" by flipping Stardust Dragon face-down or other shenanigans.
Finally, notice how Starlight Road does not negate activations. This means that the destructive effect still takes up a chain link in the chain, which is actually empty. This empty chain link causes some timing issues, which stop both players from responding to the destruction of the Card or the Special Summon of Stardust Dragon. If Terror Incarnate has its effect negated, you would miss the timing to activate its effect. If Stardust Dragon is Special Summoned, you cannot respond to its Summon (with Torrential Tribute and so on).
As a side note, a really common question is if you are able to activate Starlight Road when you activate Heavy Storm and your only other S/T Card is Starlight Road. The answer is that you can't. Heavy Storm is not considered to be destroyed by its own effect (it's sent to the Graveyard by Game Mechanics, like all Normal Spell Cards), so it would only be trying to destroy a single Card you control. Starlight Road does count itself while considering that 2 or more Cards would be destroyed.
Hopefully that clears up most questions about Road. If you have any questions, feel free to drop me an e-mail at ness00[at]gmail[dot]com.