Let clear this fact, you are not promoting your website. You are promoting your products/services and your website is avenue for it. Think of your website as a store front for your business and then from that perspective, think of way you can market it.
First, your website must be friendly and inviting.Get this free e-book on webdesign :http://www.vtnssolutions.com/e-books/17%...
Now to promoting your website ,combine both Search Engine Optimization and Pay per Click advert methods on Google,Facebook and LinkedIn.
Do Search Engine Optimization of your website and promote your website to social media such as Twitter,Facebook and Google+ etc.
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Besides tweeter, I’d like to know what the best way is to market my new website. It is a multitopic blog but I may focus on specific areas once I get more users.
How/where do I reach out to people to get them to visit the website?
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Also, once I focus on a topic area, how can I optimize my website to make it come up on google and bing search when people search my area?
Are there other sites like tweeter, I could use to post about my website?