Personal and Academic Websites give you control over your branding and image. Many institutions (including Baylor) provide space for professional websites; however, you might want to create a website independent from your institution. Some researchers have website specifically promoting their books, others for all their publications, and others for all their academic work including teaching. Others have website for the research groups and include their students on their pages. The key is to keep your website up to date.
If you want to use Baylor to host your website, go to sites.baylor.edu for more information.
If you want an independent website, you can use wordpress.com, tumblr, or about.me. Weebly/Squarespace, and Wix are either free or relatively cheap depending on what kind of package you want. BlueHost, DreamHost, HoasGator, Namecheap allow you to buy a domain and webhost relatively cheaply: just don't forget to renew/pay the dues every year.
Blogs are another way to promote yourself and your ideas. You can have your blog, be part of a blogging community, or contribute an occasional guest blog post to someone else's blog. You can even make money blogging!
If you have your own blog, the key to success is to be regular with your post which means a new post at least every month, but preferably at least once a week. Of course, you can always solicit guest bloggers to help. Not all your posts have to be academic, but they should be tagged properly. Not all your posts need to be completely new ideas either: you can comment on a paper you read, promote a tool or website you find helpful, or compile a list of links on a certain topic. It does help if you have a graphic for each of your posts and if your posts are generally between 200 and 1000 words long.
If you're not sure about blogging, try guest blogging to get a handle on your style and voice. Joining a blogging community can also help managing your time as you generally need to produce less content and are given deadlines for your posts.
If you want a website through Baylor go to blogs.baylor.edu.
Just like celebrities use Twitter to control their brand, academics can use twitter also. In fact, out of all the general social media outlets, academics use Twitter the most. By joining Twitter you can become part of the academic conversation. You can tweet about your own research; remember to put links to your publications. You can tweet interesting studies that you encounter and retweet the astute academic observations about others. Even if you don't tweet yourself, you should follow the important scholars and the relevant hashtags for your discipline. By doing so, you will keep abreast of the trends and current topics in your field.
Like it or not, people will check Facebook to find out more information about you. If you want, you can set up a professional or public page separate from your personal page where you can post information and reflections about your research. Regardless, you will want to double check and make sure that your privacy settings are set the way you want. Ask a friend of a friend to search for you to see what they can see about you.
You might also want to consider following the professional pages of any prominent scholars in your field or the group pages for your discipline's associations. Often it can be a way that you find out about awards and grants and other announcements. But keep in mind that if you join these groups, others in the group will be able to find you.