How do you add Facebook fans?

Slowly and steadily.
Start off by creating good content.
That should always be the starting point. 
Then, I recommend growing organically initially. 
Get your friends to become fans. 
Get them engaged so they will invite their friends.
As the fan page starts gaining traction or achieving critical mass, see about connecting with related fan pages. 
Get to know the person behind the related fan pages.
Collaborate.
Once you have established a sufficient base, you may want to consider Facebook ads. 
However, be careful that your Fan page is something that the targeted audience will keep coming back to after the ads stop running.

This depends on each and every company.
There are people who are willing to pay and they could use Facebook Ads but in my opinion this is so expensive because there's always someone paying more than you do.
A very effective zero-budget strategy that I personally used, is word of mouth! You can always reach out to people through friends and families and these are your first fans and they can tell others and there it goes.
It's always important to give out free things or useful information or even start controversial conversations to get more crowds.

1.
Put your Facebook page link on every marketing piece you use. 
This will help everyone who sees a marketing piece from you understand that you can be contacted on Facebook! After seeing a piece of marketing from you it will allow them to search the link with their iPad or iPhone.
2. 
Run Contests. 
Running contests are effective in getting attention for your brand while also increasing your social media presence.
3.
Images, images, images! The new design of Facebook timeline places great emphasis on visual content, so it’s important that all updates include an image. 
Brands can take advantage of this opportunity to stand out in fans’ news feeds as well as within their timeline by including images where possible. 
A majority of major brands have quickly cottoned onto this fact and it’s rare to see a brand post an update that doesn’t include an image.
4. 
Facebook post content. 
To begin a dialogue with fans, ask questions.
Although retail brand Wall Posts containing questions receive slightly lower overall user engagement (‘likes’ and Comments), this type of post generates more than double the amount of comments as “non-question” posts. 
Retail brands looking to get fans talking (i.e., increase their Post Comment rates) should use “question” posts.
5.
Offer special customer service with Q & A, live chats, scheduled 'meet-ups' with you and another expert interacting with the community.
Ask for input or suggestions for improvements and new products, or even for your next article or video.
Even though growing your Facebook likes is important don’t forget to continue to grow both your email subscriber list and Twitter followers.
Different users have different social network channels of choice and you need to be everywhere.

To add Facebook fans, differs from company to another, while some prefer to use Facebook Ads, and I think it's not expensive if we compare it with offline Ads, Radio, TV, and any other media, Some, they just create the Company / business page, and they left it and wait to get likes, in this way, they can grantee that each new like, means that the user is interested in the page / business.
Some, Do a traditional way, keep sending invites and share the page every where, and I'm totally don't agree with.

1- Speak Out: You need people to know about your page (Send invitations to your friends, Add a link to your page on your website, send e-mail to your subscribers introducing the page and why they should join, share the page link among your other social media channels.
(Free and Easy step)
2- Content is King: Share interesting diverse content, when your content is valuable to more people, more people will follow you.
It's always very useful to develop a content plan.
(A challenging and on-going step)
3- Engage: Ask questions, share exclusive news and respond to people when they post or comment on your Page.
(A step that needs time, hardwork, and open eye & mind)
4- Facebook Ads: Use Facebook advertising to grab other potential fans.
Use target options and use different Ad types: Facebook Object (Like) Ads, Page Post Ads, Sponsored Stories, Promoted Posts.
(Needs money and some marketing experience - however worthy)
5- Competitions: One of the most useful tools to increase fans (some success stories were able to generate more than 50k users).
Competitions make your fans work as marketers for you as they ask their friends to like your page and certain content in order to win the big prize.
(This step require a lot of planning, money and hardwork)
6- Your Fans: Don't run behind new fans and forget your existed fans.
Take care of them and post the content that they like, and they will help you to grow
7- Interactions: Last but not least, remember that it's all about interactions - about active users not just the big number of fans.
Make sure to have content that make the most interactions (Likes, comments, shares)

It's depend on the target people , so you can : 1.
make an AD on facebook 2.
you can share it to your friends and from your friends to friends of friends like a circle 3.
make a good design for a banner and put it in web site (an AD ) 4.
there is a web sites for make fans follow like (Fanslave) - the content of the page and the care of it make the fans like it even they share it -the good design of the cover and the page photo make the attention to the fan to like it

It depends; mostly images goes viral, share something worth sharing forward.
Add an element of "humor" to it.
Promote a promotional offer to your target market exclusive to your social media fans!

This depends if you can paid for ads and targeting the right people you will increase your fans number quickly also another method if you sharing valuable posts on your page the people like it and share it with their friends and you will get new likes it works like a network

Well, first of all,being an internet marketing expert have to focus on the major concern that Internet Marketing with respect to Social Media Marketing Fan Page /profile maintenance purpose is not only to expand the Fan Followers Connections but also to create a useful community where the users, customers even your competitors would love to share their thoughts openly with you.
Once it become a successful community, peoples would love to invite other fans to your groups, pages, this can really assists in best way to increase the Fan/Followers Connection.
Have a Nice Day.
Syed Waqas Saghir Internet Marketing Expert, SEO Consultant, Social Media Evangelist.
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Simply go to the admin panel you will find a button called Build Audience.
By clicking on it you will have two options: 1-Invite Email Contacts.
Which is a great choice if you have your own database.
2-The second option is by selecting Create An Ad.
To pay for sharing a selected post or event.