Lemme chime in as a Roy Main. I'll try to be honest about my interpretation of his abilities.
Neutral:
Roy's neutral game is an odd one, he feels like a character that would benefit from high pressure, but I find his kit mostly helps a defensive playstyle. He is excellent at stuffing out any approaches with his tilts for grounded attacks and his up B for anti-air. Roy can utilize his speed like Sonic can to force an opponent to approach him when Roy wants him to.
His main problem comes with approaching himself. He has very few options when it comes to approaching, basically what you want to try to do is condition the opponent to sit in shield and then go for tomahawks, dash grabs, and pivot grabs. Roy can get a lot off of his grabs from conditioning people to react a certain way. which brings me to my next point.
Grabs:
This is Roy's main way of racking up damage. Your first move in any match is to get a dthrow. For fast fallers, you can dthrow ->jab -> regrab -> dthrow -> uptilit -> uptilt -> upsmash/uptilt/upB, for other characters you can really only get one grab and two uptilits. This one string will instantly get your opponent in kill percent, if your lucky your opponent will attempt to airdodge your next dthrow and you can land a forward smash. Otherwise you can do some mixups with fthrow and dash attack/Up B or dthrow Up B until your opponent reaches about 90%-100% at which point...
Kill Confirms: Roy has three kill confirms that are easy enough to land my favorite is jab to upB, the up B will normally kill at 90% when Roy has rage with the exception of heavy characters like DK and Bowser. This is the move I use the most when I attempt to kill.
Your other option is to go for falling uair or first hit of nair. Either of these into a uptilt or upsmash will kill at around 120%. But I finding landing these two options to be harder than Ryo or Static Manny lead some to believe, but it could be I'm not well practiced enough yet.
After about 140%, Roy will have a very hard time killing, everything at this point with rely on reads. Your only other option is Roy's upthrow, but that will only work at around 150%-180%. You must be very careful with upthrow because it stales easily. You will have about two attempts before it stops working, then you will have to unstale it. I suggest you focus on getting little hits where you can just to get their damage up to around 170% before attempting to kill. DO NOT rely on reads for the kills, Roy can gain damage very quick if he isn't careful, I've lost many a match due to comebacks from my opponent.
Combo game:
Roy has a few true combos, Nair -> Nair, and tinder combos will normally work for Roy, especially if you get the weak hit. Sometimes, going for the weak hit is what you might want, as it helps to combo more. His grabs lead into a lot of these combos, specifically fthrow and dthrow. Then there is always Double edge dance for extra damage. Jab and dthrow both lead into UpB at low percents, and will net you a good 20% in damage.
Off Stage: Roy's Fair and Bair are good for off stage. You can catch the occasional 2 frame with a dair too. I find it's better to use d tilt and a full charge Flare Blade though. I don't like to go off stage too much with him, because if you miss you can get gimped.
Specials:
If you want an opponent to get off of you, use Flare Blade (Neutral B). Most opponents will be surprised about how little end lag it has, so don't be afraid to throw it out if an opponent is pressuring you.
Double Edge Dance (Side B) can be use to pop an opponent into the air if you use the Up variant. You can then follow up with an anti air or try to catch their landing from here. Forward Forward Up Forward will kill at the edge around 110%. Otherwise, go the Down variant for damage. This is the safest punish you can do when you just want some damage. The down variant will sometimes break shield if you pressure the sheild with a dtilt or fsmash first.
Blazer (Up B) is good for anti air. it's a decent recovery move as it can snap to the ledge easily, or you can punish an edge guard attempt if you throw it out early. Try to get a feel for when your opponent is attempting to edge guard you, and you can counter it with Blazer. Roy has some amazing magnet hands too. One thing to note, it only has invincability on the ground for the first few frames, so use it a lot in your opponents air to ground approaches. Also, you can get grabbed out of it.
Counter Absolutely rubbish, it's the 4th worst startup of any counter in the game. But it does have the highest knockback multiplier (1.35x) so it can kill if an opponent that's obviously telegraphing their attack. It also hits a little bit below Roy. So I find it useful for Cloud's Up Air.
Other Notes:
Roy is a character that does well stuffing out approaches and then reciprocating with a high damage output. A good Roy can scare most opponents. Roy is however, very easy to kill if he gets too careless. The main thing you want to do with Roy is to never take damage. Imagine playing Roy like a no damage run in Dark Souls. You need to be that fearful when playing Roy, every hit will bring him closer to death. I find most of the time I can die at about 80%-100% when I play him, so I try to avoid taking any damage that I can. Remember, be patient, rack up damage, and seal the deal early BUT try not to take too many risks.
Recommended Players to Watch: Ryo Static Manny Sethlon LD (see Smash United, my favorite Roy tbh, plays defensive Roy perfectly)