I run a business in this space. Been around for going on six years, should close out 2015 at around $3MM in sales.
how did you go about starting a service based organization, if any?
You start it just the same as any other business. I don't understand the question?
since you don't have a product in hand, how did you reach out to clients?
B2B product companies don't sell widgets, they sell solutions to specific problems. Service companies do the same thing. However, the more sophisticated service companies have figured out how to market very specific service offerings wrapped around the owned-IP of a branded delivery framework. This is why when you see the big boys (Accenture, Cognizant, etc) describing themselves, they don't really talk about exactly what they do. It's all about the outputs/benefits.
How does one go about finding what projects are available on the market?
At your stage: hardcore, personal networking. Later in the game: Still networking, but also a lot of dollars pumped into sales and marketing.
If there a specific site, where home business owners, small business post about their technical challenges and we as a company can vouch to take up the project?
Sure. AngiesList, CraigsList, Elance to some extent. But they're all garbage. You need to meeting people face-to-face: local chamber of commerce, meetups, conferences, BNI groups, social clubs, historical societies, economic development orgs, etc.
Be forewarned: selling to small businesses is a shit strategy. They're all broke, and mostly a pain in the ass to deal with (precisely because they're broke and don't know how to escape that). You want to be targeting larger businesses (at least a couple hundred employees). The only way you can get on their radar though is by specializing. My company specializes in helping migrate legacy software applications over to a SaaS model and onto a public cloud computing platform. Similar companies only do SEM for auto dealerships, or specialize in highly-scalable Magento deployments, etc. Specialize, specialize!