We do it by treating our daughters as a team. If one or the other behaves badly, then they both suffer consequences. They are 9 and 6, so old enough that they understand this (wouldn't recommend it for toddlers!). It works well, and they feel incentivised to behave kindly towards each other and work towards shared goals.
They don't feel that they get rewards or attention from us as adults by getting one over their sister. Of course, individual achievements are awarded, but we also encourage them to celebrate each other's success. We've introduced Sister Points that get granted or revoked when they are supportive/mean to each other.
When they get to certain milestones (50, 100, 200 points etc) they level up as sisters (they're currently Level 2 Sisters) and we go on a family day out (latest one will be an open top bus ride round the city).
I think we'll have to change tactics when they get to be teenagers, but so far it is working well. I had a really good, supportive relationship with my brother when I was young, and I want my two daughters to have the same.
Sibling rivalry is almost unavoidable. As a parent, the best you could do is to understand why they fight, and then try to let them sort it out. Only step in if things get out of control. Don't ever attempt some high-handed tactic like punishing them if they fight or taking sides. Instead, try to guide them to play fair and make peace after each fight. They're siblings, and sometimes siblings fight only to deepen their bond later.
It is the world of duality. It is about encouraging the sisters to share without the other one getting cranky for it. One of the sisters might by crying, while the other one might be calm and vice versa. Nothing much can be done about the latter. Encouraging sharing, and when you're out and about buying them treats - buy the exact same treat for both of them.
That's a toughie, but acknowledging each childs differences and celebrating them - with similarities it is easier to compare and thus pick who is 'better' at that, than completely separate positive points.
My kids are encouraged to share. Anything that they fight over will be taken from them for the day. So these days when they are getting in a fuss one is more willing to let the other play with it as opposed to losing it for a day.
Another thing we do is to encourage the asking for toys as to just taking/grabbing of stuff.
If one child has a toy for too long, he's encouraged to give the other a turn.
There are some things we ensure they have for themselves.