Consequences - if disappointment, mild disapproval or ignoring doesn't work to change a behaviour, relying on these can be useful, for example: if she doesn't hang up her coat, she probably won't be able to find it next time she's going out.
Distraction - when siblings argue you could say: "Why don't you both play that video game you like." If your child is in a bad mood, try something like: "Would you like to go swimming? We haven't been for a while".
Humour - can work well with school age children. If your child is whining, you could say in a silly and exaggerated voice: "I don't want to go to bed either - I want to stay up and party all night".
You may feel uncertain about how to handle giving rewards or privileges - "You can watch TV if you do your homework" or "I'll give you a treat if you clean out the garage." You might worry that your child will get to a point where she'll only behave well in order to receive something.
It's a difficult balance to strike between giving tangible rewards - for example, for doing chores - and expecting them to be done as part of a child's growing contribution to the family.
There's probably no clear-cut answer for every family and every situation. You need to work out the balance with individual children and according to the way your family is organised.
All school age children should be expected to do at least some small chores, even if it's only tidying away their own things. It will depend on your child's age and the amount of time left after school, homework and other activities. Chores could include emptying bins, hanging up washing or setting the table. If possible it's better to negotiate with your child what she might be happiest doing - this ensures having it done more cheerfully.
For extra tasks, additional to a child's regular jobs, you may want to offer some reward - this might be for cleaning the family car or weeding the garden. Just as we expect some reward for our efforts in the real world, there's nothing wrong with sometimes rewarding your child's efforts. Doing something together - a special outing, allowing a video rental, making a favourite meal - these are better rewards than money for most school age children. Make it clear this is an extra way of showing your appreciation, but that normal chores and good behaviour are still expected and not rewarded in this way.
It motivates some children to clearly work towards a reward. Teachers use gold stars and point systems all the time. You could adapt this by giving tokens or completing starcharts. When a certain number are gained, a reward is earned. It might be that you want your child to go to bed at a certain time without an argument - each time she manages this, she gets a star. After an agreed number, you give a reward.