When deciding what to wear with a gray cardigan, it is helpful to think of the color gray as a neutral and not a color. If you think of your gray cardigan as being neutral, you're halfway there. A neutral is a basic color that you can marry with practically any color you wish. Neutrals such as cream, white, and black are used as a backdrop to color. Once you wrap your mind around this concept, dressing up that gray cardigan will be easier than you think.
The first rule in deciding what to wear with a gray cardigan is not to over think it. Simply go to your closet and pick out some of your favorite shirts. Some may be button down, or you may choose a turtleneck tee shirt. Try them on and see how it looks.
If you want to dress up a gray cardigan, think about what goes well with gray. What colors make gray? You may want to try a black pair of trousers and a white shirt with a gray cardigan. Use an accessory like a bow tie. A small accessory like a bow tie can change the look of an outfit in a heart beat! If this is too boring for you, branch out and change your shirt to a plaid shirt with a little yellow or blue in it. Depending on the print, a bold plaid will look fantastic.
When dressing down a gray cardigan, think in terms of subtle colors, like light blue or medium washed-out green. Give a small plaid shirt a try. Wear a medium wash blue jean. Leave the cardigan unbuttoned to showcase a really cool rustic belt. Wear a scarf that match the colors you chose to tie the whole outfit together with the gray cardigan.