Pretty much the same way you do SEO for any other website.
The difference is the web hosting industry is horribly over saturated. There are new hosting "companies" opening pretty much every day. ( and some closing almost every day).
There are many companies that have been at it for many years and have thousands of backlinks, tons of articles, and some with marketing budgets of many thousands of dollars a month.
You simply are not going to compete in the web hosting industry on SEO and paid advertising alone. It take a lot more work then just that. You have to put yourself out there, talk to people, help strangers, and be willing to go the extra mile to get a few customers!
If your hosting business is relatively new I would suggest using parasite sites as a means to attract business and as a means to get your marketing message in front of targeted prospects.
Here is what I mean by that:
Go find a blog that has a lot of authority that you might be able to guest blog post on. If you can't find one or if you don't know how to get someone to let you guest post then you might be better off looking for a freelance writer who already has authoritative places they can write articles for.
Then pick a long tail search phrase that will be a little bit easier to rank for - something like - "best hosting company for niche blog" that will be an easier phrase to rank for than something like "best hosting company".
Then write or have a talented freelancer write an exceptionally detailed blog post that explains what a person should look for when they are analyzing which web hosting company they should go with if they are looking for a site to host their niche blog. Make sure this is an epic blog post that is really well written with lots of personal detail and personal experience based content included. Include some high quality graphics in the post. Make sure the article mentions and links to your web hosting website.
Once that post is published, go buy a few dozen assorted social media shares from somewhere cheap to serve as social proof that other people like the article. Then go promote that article using whatever means you have at your disposal. Build links to that article using whatever means you have at your disposal. Don't spam it though.
You can repeat this process using different writers targeting different long tail phrases. This form of content marketing will slowly start bringing in trickle traffic for your website and it will also start helping your site rank better.
The reason you want these types of articles posted on other authoritative websites is because those articles will attract more search engine traffic because they will rank higher on a site that has more authority than yours. And those articles are more likely to achieve natural links than they would be if you published them on your own company blog. When people read those articles on those other websites, a small percentage of them will be interested enough in your hosting to come to your website and see what you have to offer.
Yes it takes real work. So does anything that is worthwhile in life.
Not to be a dick, but I'm going to likely save you a lot of time. Forget about SEO for a web hosting site. If you are asking how to do it, it is pretty obvious that you do not have the skills to compete in a very difficult market space. You are likely just going to spin your wheels for months and wonder why you are not making any money.
I would figure out a way to make a name for yourself on social media instead, and hope to attract traffic that way.
I would also visit a site like WHT and setup a special offer there. You'll get way more traffic that way than dabbling in SEO.
I haven't read all the answers here, but from my experiences promoting a hosting company (was a reseller at one point), it's best to use social media to promote your business. Web hosting is one of those things where you can always make a sale if you have awesome deals and can provide reliable service to your customers. If they feel they can trust you, you will make sales.
SEO is going to be extremely difficult as there are tons of hosting companies, maybe promote specific landing pages to targeted groups of people. Such as "New York website hosting" or "Drupal web hosting". I don't know how many people search for these but you need to get specific, or start paying for PPC traffic.
In all the SEO work that I have done (which is quite extensive) I have never seen a single situation where I would recommend what you guys are suggesting to a person who is trying to rank higher. Branding and SEO are two totally different things.
It is very common to have an excellent brand (worldwide well known brand) and still not be able to rank for valuable keywords. In most of those cases, branding has nothing to do with SEO at all.
Let me offer you an example.
If you go to Google right now and search for this phrase - best fast food restaurant franchises - That might actually be a phrase that a person who is researching buying a fast food franchise might search for. If you perform that search you will see that there is not one single well known fast food franchise brand that ranks in the top ten for those search results.
If SEO was just about branding then you would see companies listed there like McDonalds, Burger King, Subway, Taco Bell, Wendy's, Tim Horton's, Kentucky Fried Chicken, etc.
Yet, there is not one single one of those names listed there. And the reason for that is because branding and SEO are two totally different things.
Having a strong brand will make your SEO efforts easier because it is easier to generate publicity for something people already know about. But increasing your brand awareness will do absolutely nothing "by itself" to help you rank better. You still have to do all of the SEO work whether you have a well known brand or not.
If one of those fast food franchises wants to rank high for that phrase I mentioned, then they will have to create a page on their website that targets that phrase using all of the traditional SEO practices (on-page SEO, site-wide SEO and link acquisition). If they don't do that, then chances are they will never rank for that phrase.
SEO does not depend on branding at all. If your SEO strategy is to increase your brand awareness, then you will be outranked from now till forever by the most unknown competitor who did actual SEO work for their website/web page.
Although fahadrafiq and speedywriters comments above were just plain dumb, I largely disagree with Ted.
Branding absolutely can be a part of an SEO strategy, and in a lot of cases it should be.
It certainly should not be the primary strategy, but there is a lot you can do with a solid branding campaign.
For example, I have a client whose brand was only searched about 110 per month a little over a year ago according to Google's Keyword Planner. Now that same brand gets searched over 3,000 times per month. It is a small niche, but that is pretty profitable search volume for them.
I have a confidentiality agreement with the client, so I cannot show it specificially, but the product relieves a certain ailment. Because of our branding campaign, there are a lot of search terms about that ailment where the product name now shows up as one of the suggested searches at the bottom of the first page of the SERPS.
We did a good job of increasing the brand awareness to the public as well as making the search engines feel that this product is synonymous with the solutions to the problem.
Branding was not the only focus though. We have something like 36 other keywords in the top 3 and another 40 or so in the top 10.
All of that being said, for your typical IM'er this is far too advanced to pull off, and they would not even know where to begin. It is also not cheap. But to say that branding and SEO cannot go hand in hand is just untrue. It absolutely can.
Here's what comes into my mind after reading your title.
If I was at you, I'd contact with the coupon code sites mostly the authority ones and offer them a good discount deal for their site visitors and also set the different affiliate commission margin as per their site credibility. This way you'll get maximum boost to your hosting company in a shorter period of time. It takes time and efforts to do it, but trust me it works.
EDIT: Also you can apply this technique on quality blogging sites as well.