Creating a paper cut-out look is quite easy using the Appearance Panel and the Width Shape tool.
We are going to create some weather icons for fun and use the Graphic Styles Panel to capture these setting and apply them easily later.
Start with a circle. holding SHIFT to make a perfect circle.
Use OPTION and click and drag the circle to create a duplicate and mov e it half way over the other circle.
Use COMMAND + D to duplicate it further.
Copy another set above the existing set to create a cloud.
Use the Pathfinder to Unite the circles, or chose Effect>Pathfinder>Add.
Open the Appearance Panel from the window menu. Add a white stroke, 9 pt, and click on the stroke OUTSIDE of the path by checking the button highlighted in red in the stroke panel.
From the bottom of the Appearance menu, choose the FX menu. Stylize, Drop Shadow.
Apply a drop shadow to the shape.
Make sure you drag the drop shadow effect UNDER the fill section of the Appearance panel or else it will apply the drop shadow to the Stroke, just like you would move layers in the layers panel from one location to another.
Here is the result. Stroke is outside the shape and the drop shadow outside as well. If you apply the drop shadow to the stroke, it will appear on top of the fill.
Open the Graphic Styles Panel from the Window Menu and drag the cloud into the Styles Panel and it automatically adds the attributes (Stroke, Fill, Drop Shadow) into the Panel for future use.
Draw a circle and click on the new Style you just created in the Graphic Styles Panel and the circle will have all those attributes.
Select the sun and change the fill to yellow, it will keep all the other attributes (stroke and drop shadow). Send the sun to the back. Then add a few stars and click on the style from the Graphic Styles panel to apply all the attributes to the stars, then change the fill color to dark blue.
Add some rain drops. Inside they are filled with white then have an inner glow added.
Add an Inner Glow to the Rain Drops. Chose the FX button on the bottom of the Appearance Panel and choose Stylize>Inner Glow. Set the fields as shown with a light blue fill. You can drag the new rain drops into the Graphic Styles Panel to capture the rain drop settings for future use.
Drawn an arc, add a white stroke to the arc, about 20 pt.in this case.
Click the FX button on the Appearance Panel and choose Stylize>Feather. Set the feather on the stroke to .2 cm.
Use the Width Shape Tool (SHIFT + W) and pull out the center handle on the curve to make it wider, and pull in on the ends to make them thinner.
Here is a close-up of the handles you get using the Width Shape Tool on the Path. The handles are what you pull in and out to pinch or widen the lines.
Drag the feathered arc into the Graphic Styles Panel.
Make another arc on the clouds, then click on the Feather Style you just created in the Graphic Styles Panel to get the arc to feather and pinch at the ends.
And that is how you make some simple cut-outs from Illustrator and save the Graphic Styles for later.