When you say "increase the number of backlinks fast for your website" I get the impression that you want to build hundreds of links or more back to your website as fast as possible. And I question your reasoning and thought process for wanting to do so.
In most cases, of course it depends on your situation, you really don't need that many links. You need powerful links. Not lots of links. You need powerful permanent links that keep passing massive amounts of link juice to your page/website day after day pretty much forever. If you get a handful of them that are juicy enough, that is all you might need. Again it depends on your situation. If you are competing against well entrenched pages on big brand websites, then you will need more link juice than I described, maybe a lot more. Everything depends on your situation.
It also depends on how many pages are on your website, how many of them you want to rank high and how deep into your website those pages are. You need to send enough link juice (a.k.a Google PageRank) directly to the pages you want to rank well. And you do that using regular "followed" hyperlinks that hopefully use anchor text that is relevant for the keywords you want to rank for.
There are various ways you can go about getting those powerful juicy semi-permanent links. You can buy existing websites or domains that have this juice and redirect it to your website using 301 redirects or by publishing content on that site and linking back to your site. You can buy links from any number of places being careful and selective to make sure you aren't buying from a network that is about to get nuked. You can use tiered linking where you produce your own high quality page on a Web 2.0 site or a guest blog post or some other website you control and then push link juice at that page so that it passes that juice on to your page/website. You can hire an SEO service to build links for you if it is worthwhile. You could build your own network of small authority sites that you use to link back to your own websites.
Those are the easier ways. There are also harder ways that are difficult to execute well.
If you want to work your ass off and do things the white hat way then your primary form of link generation is going to be to create some form of link bait. And then promote that link bait to the people who are most likely to link to it. That link bait can take many forms including a controversial blog post, an epic tutorial blog post, an infographic, a piece of free software, a funny video, a recorded interview with a popular celebrity, a written interview with a celebrity, a published solution to a major problem that everyone faces in your industry, etc. Use your brain. Come up with something new.
If you want to make it easier to earn natural links to your websites, then start making friends with other bloggers in those fields. Bloggers link to their friends. You could create an entirely separate blog website that you use to meet other bloggers. Write lots of posts and link out to other bloggers and talk about those other blogs. Those people will like you for promoting them and some of them will feel a need to reciprocate if you promote them enough. That is how you make friends. If you have a network of friends who own blogs, then it is easier to reach out to them when you need a favor.
Inevitably, getting white hat links involves reaching out to people and talking with them one on one. It involves a lot of that. You have to do that to at least get the ball rolling. You can reach out to them however you want to. Some people use email. Some use social media. Some will visit another person's blog and comment on their blog to start a conversation with them. Use whatever means you can come up with.
