It all depends on how good you are, really. To compete in such an industry (That is filled with awesome designers/developers with years of experience) you need to be both a great designer and an even stronger coder (as you mentioned web designer), and then brand/market yourself well.
However, if you're going to focus on a particular niche, you'll find it to be easier and it wont weigh mainly on your skill level. Say you wanted to focus on small business owners, mothers for example, wanting to design, brand and launch their blogs/sites, while that's a large market, it'll be easier for you to compete in, rather than throw yourself into the deep end and compete with those that have had years of experience on you.
You'll need to start with a plan, focus on who you want to target, who your potential clients will be and what you want to offer as services. Try not to spread yourself thin and instead, focus on only what you're really good at, anything else you can provide as extra services once you land a client.
Then you need a site, obviously, and a portfolio. On the site detail your services, make it easy for them to acquire them, and make sure you update your portfolio with new work.
Say you want to take on logo design, you should have at least 5+ logos in that section of your portfolio, same goes for other sections, banners, web design, etc. It's always good to add recent work done so that you don't end up with an outdated portfolio, it'll also give return customers the sense that you're being hired and that will only build their confidence in hiring you.
Once you have a site and a full portfolio, sign up to different showcase galleries and make a profile. Then submit your work for more exposure. Sites like Behance, Coroflot, Creattica, Logogalleria, Logofaves, and other sites where you can share your work and get feedback/votes in order to build your online presence as a creative.
From there, just try and land work, either by contacting people on job boards looking to hire someone, through twitter, crowdsourcing sites and try to place threads up where you can on forums providing your services.
I would also focus on the niche that best suits you, if (for example) small home businesses run by mothers is your ideal potential client base, then join forums dedicated to these small business owners, mother boards etc and find a section where you can advertise your service. Make sure not to place it in the wrong place and get mistaken as a spammer, your reputation is what will sell your service for you in the long run! Help people our, place your links in your sigs as you do on here and give advice on how people could go about fixing their site, advertising their products and you'll generate interest in your service indirectly.
Build it up from there.
Anyway, good luck with starting your new business if you decide to go through with it!
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