There are lots of things you can do improve your game, but more importantly practicing the same champ over and over has its highs and lows as well.
One of the big things it sounds like your brother is having a problem with is the balance in damage given and taken. Now, since he is still new to the game and learning the match ups, he needs to continue to experiment and figure out what will work for him. Every champion cannot be played the same by everyone, that is basically why there are different levels of leagues. A Gold 1 Riven vs say a Gold 1 Yasuo might win that match up, but struggle against say a Riven vs Darius. Then lets say a Bronze 1 Riven loses vs the Yasuo and wins against the Darius, its only a matter of time before he understands his limits and match ups.
Learning damage outputs is probably one of the most important parts of the game, and the more you play the more you will get better if you are practicing the right things. A really good tip I would have to suggest would be to try to avoid taking as much minion damage as possible, those little devils dish out way to much damage. Something I like to do is I wont harass my enemy until half of the minions in the wave are killed, leaving only the casters left to inflict the lesser damage of the two evils but I will not harass on canon waves.
The next thing I would have to say is he needs to learn what runes fit his play style and what type of build you should go for. I personally prefer to get to max 40% CDR as soon as possible, so I can dish out those spells faster then my enemy gets their cds back up. Maybe something like this -
>> 
= 
+ 
>> 
+ 
Those will almost always be my first two items that I would get on a Riven, or any type of bruiser for that matter. A bruisers job is to get in there, do bunch of damage, take some damage and then get out and let your team do the rest.
He needs to get creative with Rivens spells. When you watch majority of Riven players, they usually just smash all their skills and then get it, but thats really not the best way to play her. If you know what Rivens passive is, it causes her auto attacks to do increased damage every time she casts a spell. So if you add up all her spells, her passive stacks would consist of 5 or 6, i cant remember if her ult casts as a passive. So if you mash her spells then you have 5 extra attacks that do bonus damage right? wrong! She can only hold 3 stacks at a time, so that means that you are losing damage.
My skill cycle is usually - E-Q-Attack-Q-Attack-W-Attack-Q-Attack then cast your ult and that usually will kill just about anyone, unless they are a tank like a poppy, so you would have to probably get her down to lower health before you combo her.
Like I said earlier, playing the same champ over and over has its flaws as well. To truly know how to play against other champs, you have to know how they are played. He will never get the experience he needs if 100 of his games are played on the same champ, because watching someone play and playing someone are not the same thing. So I would suggest taking a break from the same champ, and mixing in some of the champions he is having a hard time playing against and once hes gets in the mindset of how that champ works, he should fair off better when he returns to Riven.
