Skirts make the perfect finish to every outfit, more versatile than pants and far more fun, they can go with just about everything. However, it is important to style your skirt appropriately for the occasion as you can dress it up or keep it casual.
For a summer or spring day where you want to wear your skirt out and about on a brunch or shopping trip with friends, keep your style low-key. You can compliment your skirt with a tank top or t-shirt in a basic, neutral color (like black or white) or you can match a top to a color in your skirt. If it's chilly, layer a larger sweater over it in a color that compliments. Make sure the top is casual though or you can come off as a bit too formal. During the day, looser fitting skirts often work better. In terms of footwear, pair your skirt with flats, sandals, espadrilles, or a cute pair of casual wedges.
For night, tighter skirts work better. Pair your skirt with either a looser fitting top, like a crop top, if the skirt is high waisted, or a top with fun details, like beading. For footwear, heels are definitely the way to go. Try a pair in black or a color matching the skirt.
For work, you should pair your skirt with a blouse or a tailored shirt, like JCrew's Perfect Stretch Shirt. Lower heels or detailed flats will compliment the outfit well - try kitten heels. A nice blazer can also add a more professional touch to a fun skirt and pearls can do the same.
Regardless, remember to have fun with your skirt and to mix it up - there are so many ways to wear a skirt, so do not limit yourself.