Some ways as I know are below:
Blogging is one of the best ways to promote your website online! By writing a blog for your website, you give a reason for visitors to keep returning to your site and keep up to date with your latest posts. It also helps search engines to crawl your site more frequently, as they have to update your latest blog post entries, which ultimately helps you rank higher in search engine results pages (SERPs).
You need to produce and include lots of unique content for your blog, such as; Infographics, Top Lists, How Tos Tutorials, Viral Videos, etc. Try to remember to be clear and concise in what you are trying to convey to your readers within your blog posts, don't waffle.
To help you promote your blog, submit it to niche blog directories and blog search engines.
If you're not very good at writing content for your blog, then you could always hire a guest blogger for your blog and ask him/her to write precise and unique content so that your blog can gain more credit from a search engine point of view.
2. Blog Marketing
Post comments on other blogs within the same niche as yours, which allow you to add a link in the comments section. These links can then be crawled by search engines, helping to point them towards your site. These blogs are commonly referred to as "Do-Follow" Blogs (Just like ours, where you can comment below!).
3. Forum Marketing
Find forums online that are related to your sites niche and get involved within that community. Reply to threads, answer peoples questions, offer advice, etc. This all helps to build up your reputation as someone who is an expert within that niche. Try to use "Do-Follow" Forums so that you can include a link to your site within your signature, which helps search engines crawl your site.
4. Search Engine Submission
Search engines will eventually find your site online, but that can take a while. To speed everything up, you should submit your website to the most popular search engines like Google, Yahoo, Bing, etc.
5. Directory Submission
Many people may say that directory submission is dead! I believe that it isn't as you are increasing the likely hood of people seeing your website. It is purely based on how effectively we are selecting those directories and how efficiently we are choosing the category for submission. You could submit to general directories, but for maximum effect, you are better off submitting to niche directories. Of course, I agree that it gives quite delayed results, but it is worth doing it.
Hope this helps.