1. Define a balanced room.
In order to know where to start, you should know what the end goal will look like. A balanced room is a room that has equal amounts of furniture accent pieces, and decorations on either side of the room. This also means that if you have a tall plant on one side of the room, you should have something tall on the other side of the space to balance it. Here are two pictures - the first is of a balanced room, the other is unbalanced.
See how the sofa is balanced by the two chairs, the built-in bookshelves are on both sides of the fireplace, and there are two of everything.
Notice how the room is unbalanced? You could draw a line from the top left corner to the bottom right corner of the picture and see how the entertainment stand (with the sculptures) is taller than the mantel (with the accent pieces) is as tall as the plant. There is also an end table on the left side of the room, and nothing but a gate on the right side of the room.
2. Rearrange furniture
Just because your room isn't balanced, doesn't mean that you need to spend a lot of money trying to balance everything. Sometimes, just moving furniture is all you need. Don't be afraid to take furniture from one room and move it into another.
Good luck with balancing your rooms!