Facebook makes it easy to invite the Page Owner's friends by using "Build Audience" --> "Invite Friends..." How can those who like my page invite their friends?
Tell them "Invite your friends and all of people on your friends list to my page or I'll snap your neck, kthnx". No, don't do that but that's a perfect example except nicer words. Make a wall post on your page asking everyone to invite their friends to your page if they don't mind doing so. They can invite the same way you invite.
When someone joins the community, inbox them a "Thank you" note and ask them to invite other people too. Some would respond to that, many won't. But something is better than nothing.
You can also ask them to share some of your posts this way their friends will see them and who's interested will come on its own
Engage them with something interesting and provoking before doing all the described. Fire some discussion. Post something amazing or unusual couple times to keep them hot and strike with your request!
Give them incentive such a giveaway or competition. Most people these days won't do something just because you ask them to, even all it takes is clicking a button. Give them a reason that will benefit them, whether it's public recognition, free products, etc.
I read many of answers which are very true but works slowly. If you are inviting all your friends to like your page, you need to click on "Invite" hundreds of time. I have downloaded one script: http://pastebin.com/ZJZpmpFg You need to run this script in your browser's console section. It works perfectly for my page. Hope it'll work for you as well. Usage: 1. Open your Facebook page. 2. Open Console section. [Chrome user press F12] [Firefox users Ctrl+Shift+K] 3. Paste this JavaScript code and press enter. (http://pastebin.com/ZJZpmpFg) Wait for magic. In a few seconds all of your friends are invited to like your page. I've used this method many times and it's perfect. If any issue is there, let me know. Surely try to help you through it.
They can share your page link to their wall or timeline. That is the simplest thing to do but you have to engage with them for them to do the favor.