How do IT companies find their customers?

You generally start in bidding platforms and in your local area. Contact businesses and see if they need one of your services. The critical part is to develop trust to retain customers. If they enjoy working with you, you will be first on their call list, and they will be happy to refer you to more prospective customers. Repeat clients by far are the most reliable source of income. So expect it to take time, don't go looking for shortcuts.

We would recommend tapping into the freelancer market at Upwork.
Toptal. ...
Elance. ...
Freelancer. ...
Craigslist. ...
Guru. ...
99designs. ...
Peopleperhour.

You can try approaching small/medium sized design and social media marketing companies. Usually they will not have in-house developers.

You can run PPC campaigns to get quality leads for your business.

Both Apple and Google have app stores so why don't you already have apps the public can view/use?

What niche/industry sector are you targeting?

What size company are you targeting?

Can you describe your ideal customer?

If you want to deal with larger companies, what job title or position would be the one to approve working with you?

I don't expect you to answer these questions on a public forum like this, but you need to know the answers.

Once you do, start compiling a list of companies that fir your ideal profile. Craft a lead magnet (often called a white paper in the circles you want to be in). This is not a sales letter, it's a demonstration that you know what you're talking about. For example, a short, 5-10 pager called "7 Ways Having Your Own App Will Boost Your Bottom Line" would likely work. Then start making individual contacts with the person at those companies who could hire you. Offer them a free copy of your white paper in exchange for their email address. Follow up with a simple, non-threatening (i.e., non-salesy) message like:

Hope you found our white paper useful. Thanks for requesting it.

We develop high-quality applications for companies like yours, on time and on budget.

Should we be talking?

Best,

[Company contact name & info]

PS - Do you mind if we keep in touch from time to time with more valuable information like our white paper?

Once you have a few projects under your belt, you can start sending case studies. Until then, you can drip more content on them (articles, industry news, etc.)

It's more time and labor intensive than simply scraping a list of emails and sending a generic "got any work for us" cold email, then wondering why no one answered.

Most smaller or newer tech companies typically start off by finding projects on freelance sites and online marketplaces (e.g. Upwork, Freelancer, Total, Guru, Craigslist, etc.) since those are customers actively searching for their services and they can bid on the projects. These projects are the quickest way to build your portfolio and clientele. Some also use email marketing as well.

More established tech companies with larger budgets typically find clients through business development such as cold calling, business networking events, joining tech-related groups and LinkedIn to connect with potential customers. They also will use inbound marketing and PPC to generate traffic to their website.

As a new tech business, I'd recommend starting off on Craigslist and online freelance marketplaces to bid on projects, using email marketing, and meeting businesses in your local community through networking groups and your local chamber of commerce.