Yes ago when having a website was the BIG thing I owned a website design company. How I attracted new business was I look for businesses that already had a website that was bad. I would design the first page and present it to the owner, I closed about 8 out of 10 of them. I also went where business were ie. Chambers of Commerce, Sites like this one, etc. Also make sure your stuff is prefect so when people come to you they want what you have.
The best way to get project leads for your design business it to make sure previous clients are happy with the work you gave them and can refer you to their friends or colleagues. You could even occasionally send out emails or snail mail postcards to previous clients telling them for every new client referral that they send you and completes a project with you, they get 10-15% off their next project. This would incentivize them to talk to others about your design business.
The core issue is visibility.
You have to get on the radar of your potential customers. Depending on your business model- contracting and freelance, similarly secondary business-to-business contracts with establish designers/firms, collaborations are options.
Creative work for nonprofits and social initiatives (paid and unpaid), frequently nonprofit stakeholders have ties to business communities however are emotional vested in their nonprofit causes
Display and promote your current profilo. In your contracts discuss with your clients the future use and marketing/promotion of your work (an them). For some clients you may select to retain all or some of your design's intellectual property or not (depends on the client). Your client may promote you such and such designed by Azana on the materials-
They are more options depending on you and your situation.
The best way will always be to keep doing kick-ass projects for your current clients and get that word-of-mouth generating for you. You never know what kind of leads will come your way. There are a bunch of different sites for you to check out, but I frequent Thumbtack.com because it's the closest service design I've seen for contractors that is hands-off the work process, and is 50/50 on the client to designer relationship. Most crowdsourced sites like 99Designs, Fiverr and DesignCrowd are marketing towards the clients and ultimately rip-off both clients AND designers. So don't go for those.
But ultimately I'd say it's about becoming as known as possible. Email an online portfolio of your work to different places, maybe even get one printed and mail that. Perhaps you create a shirt design that gets noticed. Hell, maybe you find a place you'd love to redesign and you design a concept to mail to them in order to grab their attention. If you're big into social media, keep posting or blogging. If you're not, then start!
To get started, you can try freelancer.com, guru.com, vworker.com etc sites.
EnggDeveloper Mark, Cloud based solutions at www.developermark.com
It's best to be clear about what you design, both to us and to your prospects. Do you design roads, or graphics, computer software systems?
Then, when people ask "What do you do?" you say "I design logos for businesses" (or whatever it is you actually design). Make sure you have a portfolio (either with you or online) that you can show to the people who say "Can I see samples of your work..."
Here's an article with more ideas for Answering "What do you do" http://www.improvandy.com/elevator-pitch/answering-what-do-you-do/