1. Let them make choices- This is hard sometimes as a parent, but children need to practice making choices. You even need to let them make bad choices, so they can learn from the consequences. For instance, you might say, "Johnny, it's pretty cold out today, I don't know if you want to wear shorts to school." Then if they still insist, you can let them do it, and they will learn. But let them choose their outfits and the way they wear their hair. Let them choose their activities. Give them a list of activities to choose from that will work for your schedule.
2. When assigning tasks, also let them choose. This works well to avoid power struggles about chores. If you have a list of tasks they can choose from, it will go much better, as they feel the power when they pick the task themselves.
3. Take yourself out of the equation. For example: set a timer or play some music if it needs to be done in a certain amount of time. Then they don't have to fight against you...they are working against a timer, or trying to finish before the music does.
4. Let them choose WHEN they do things. Perhaps you can't give them a choice of what to do, but you could give them a choice of WHEN to do it.
5. While they make choices, teach them the consequences of the choice they are about to make. Of course, if the consequence is unsafe, then you must step in and take the option away. But you can direct them to new choices. Re-direction of their attention is also an effective tool, especially with young children.
6. Teaching them to do things for themselves is another way to take yourself out of the equation, so they don't have to feel like they need to fight against you. I know a mother whose son fought eating at dinner every day. Finally she taught him how to make himself a peanut butter and jelly sandwich. Each night she put the peanut butter and jelly at the table, and after he tasted two bites of the food, he could make himself a sandwich. This solved the problem! No more power struggles!
I hope these things ideas will help reduce the power struggles in your home as well!