Likes alone on Facebook will not enhance your business, and as mentioned by other users they have systems in place so paid advertisers will get their content appear in user's feeds a lot more often than those who do not pay. I would advise posting content that gets users to engage, sounds silly, but this is why a lot of businesses on Facebook post "caption competitions" just as an example.
Well, I mostly try to "like" people with similar interests, other low-profile designers, and they usually like me back. But this strategy is effective, if you only want to raise the overall number of likes and shares.
If you want to increase leads, and actual customers, then I must agree, that Facebook ads are pretty effective, just make sure you target not your friends (if your friends wanted to order from you, they would, but choose specific audience, where you might find your actual clients.
A good method is publish a good article on your website that is relevant to your target audience then create a link from Facebook as a post, make it engaging then promote the post to a specific area, say around your local area.
The best way is to work on useful content and then share it on Facebook. Asks your friends and family to like your page and share the article if they like it. It will help you earn relevant Facebook likes. Also, posting in the related groups or pages might help you, but it is advised not to spam the pages and groups and abide by their policies. Also, if you want to invest some money in this, you can use Facebook's plan to promote your page and you can get 500 likes in a week, if you're pages has good and relevant content.
I would agree with the latter part. Previously, I used to work in a Software testing company, so it was pretty hard to engage audience or getting likes for the page, that talks about "software testing" and going for the Facebook plan might be the right thing, as to target the right segment.
But now i work in a company that sells garments and I ddn't use any Facebook plan and I have around 1k traffic daily landing on product pages through Facebook and also this page gets around avg 500 likes in a month. Most of the people that visit page, tag their friend on a particular post and this is how this chain works.
So, it depends on product, facebook marketing is largely effective too, but sharing content with the friends does help too.
Using Facebook ads is pretty much the only way to gain new, relevant likes to your page now. You can share all the content you want, but Facebook decides who sees it. Without paying for sponsored content, only about 15% of the people who like your page will see it organically (thanks Facebook), and only a small percentage of them will act upon your content.
As has already been said, organic marketing on Facebook is tricky. There is a movement towards social media "privacy" now, too (paradoxically...), so there are active filters working against anything that isn't 100% relevant. Paid is the way to go, but even then, I think there are better assets out there to explore. Facebook is too close to home for people - they'll be more reluctant to engage with your brand in this unprofessional context.