What's the best way to market a website development company?

The best way to market a website development company is to showcase your work.

I suggest having a great website with a great portfolio. If you do not have many clients and are not sure what to put into your protfolio I would suggest that you develop some home pages that you can showcase so that potential clients know what they can expect from you. The best way to create a great protfolio is having different niches showcased ( retailer , blog , social media , club etc. ) so that you can appeal to the wide variety of possible clients. Other thing you should do is to have a great marketing text written on the website that points out why someone should pick your company over the other.
After you have done the preparation and are ready to market your website with you services to potential clients you should set up a strong social media presence on Facebook , Google+  and Twitter (other social networks can also be useful but these three are a must). You would than have to focus on specifics of those social networks that you have chosen to use and apply to your specific audience. On Facebook you could post some of the more personal stuff from your brand that can be showing a regular work day or team building that you went to. On Twitter you should post industry updates and your blog posts. On Google+ you should focus your effort on communities and and answering other peoples questions so that you build trust in your company and ability.
In the end no marketing campaign has any point without sales and I would strongly suggest having at least one person who's sole job would be to sell your services.

Hope this helps you. Fell free to ask if I can help you further.

I believe every company should have a blog. It's a great way to really get to know your audience and for your audience to get to know you.

There are many ways. Search Engine Optimization and Social Media
Optimization can prove beneficial. It’s widely used these days and many people
are promoting their business through it.