Standard Rainbow Background.
1. Make sure you're on an empty layer.
2. Fill the entire empty layer with a rainbow pattern, you can use any texture, width, and direction to do this. I used the biggest width and a solid texture and made them diagonal.
3. Give it a border of any colour, I used black.
4. You can add in shapes, I put a heart in the lower right corner.
5. You can also put a texture over all of it, or just a section, I used the polka dot pattern over the entire thing, to match with the bow on her dress.

Disregard this, I clicked upload without meaning to.

Cartoon meadow background.
1. Make sure you're on an empty layer.
2. Make sure the empty layer is last.
3. Fill the empty layer with a shade of blue.
4. Use a green colour to make the ground and maybe add a hill or a few.
5. Use white or a very light pink or blue for the clouds. To make clouds, I clump together circle shapes.
6. Make a new layer and place it before everything else.
7. On that new layer, use a darker shade of green than the one you used for the ground, and make some grass. Add flowers of your choice and colour.
8. I add eyes and blush to the clouds, and add eyes to the hills.

Starry night background.
1. Get a dark dark shade of purple or blue, and fill an empty layer with it. Make sure that the empty layer is last.
2. Take a dark green colour, and make the ground. I made it curved to look more natural, like a hill.
3. Get a very light yellow colour and make a circle, take the background color and make the moon a crescent shape.
3. Take white, and make sure the width of the brush is 0, make dots all over.
4. Take a lighter version of the sky colour, and make dots all over.

Simple Background with shadow.
1. Fill an empty layer with a colour of your choice.
2. Pick a colour and go around the edges with that colour to make a border.
3. Use that same colour you use for the border to make some patterns.
4. Pick a colour for the shadow and go around the outline of the character.
5. I do this all on the same layer.