There's a feature on Facebook advertising that is easy to overlook but vital for an effective Facebook advertising campaign. It's a little button that prevents your ads from showing to current fans of your Page. Why is that button so important? It keeps you from wasting your money on clicks or impressions from people who are already engaged with your Page, and prevents them from getting annoyed with you for spamming.
Your basic Facebook ad is designed to drive fans to your Page. It may say things like "Like our Page for info on our business and industry!" When your page is showing to "Anyone" rather than to "Only people not connected to [your Page]", you are wasting impressions, and potentially clicks, on your current fans. At best, your current fans will ignore the ad, since they've already liked you. They might click on the ad, confused by why they're seeing it. At worst, they will unlike your Page because they're being spammed by unnecessary advertising.
So when do you want to show ads to "Anyone" or "Only people connected to [your Page]"? When you have a specific message that would apply to current fans as well as potential fans, such as a special offer or promotion, or to remind current fans that you're still out there. It may be especially helpful to show ads to only current fans if you're providing a special offer only to existing fans. To make sure that your current fans see your posts, because Facebook's EdgeRank means that only a small percentage of them will, you can show Promoted Posts to only people connected to your Page. Targeted, specific activities like these will make sure that your advertising money is well spent.
No matter which Connections button you choose, the important thing when creating any Facebook ad is determining your objective. Once you determine what that is, whether it's getting new fans, improving your Page reach or engagement, or promoting a special offer, you will be able to target the appropriate audience.