I've already completed my first grueling year of the PhD program, and graduation is still a yet to be seen light at the end of the tunnel. I'm very sure that academia is for me, and I really want to obtain a tenure-track position in my field (computational science). I know that universities often look very highly upon doing a post-doc and accumulating plenty of journal publications. Of course, open faculty positions are extremely competitive and I'm sure that everyone applying for them have those qualifications already. I'm curious if there is anything else I do as a graduate student to help maximize my chances of getting a Tenure-Track Faculty position in the future?
I don't think there's anything "special" that's unique to applying to academia that a graduate student can do to increase the odds of becoming a professor in the long run, particularly if one is going to do a postdoc later on.
The two areas that might help are:
Gain teaching experience that goes beyond the standard "recitation section" leader—that is, into actual lecturing and other forms of direct interaction with students, as well as formulation of assignments and examinations. This might make a difference at schools which are more teaching-oriented rather than research-oriented.
Formulate a well-defined scope for your future research activities, and also develop the tentative outlines for the first few projects that you'd start in that field. This is an essential part of any professorial application, and the sooner you start working on it, the more polished it will be when you're ready to apply for positions when the time comes.
Beyond that, what makes someone a good candidate for a postdoc are essentially the same qualities that will help in being a good candidate for a professorship later on.
I think the single thing that most helped me get a tenure-track job was that during my postdoc I gave lots of talks at conferences and in seminars at other schools (something like 30 talks in 2 years, including those I gave at my postdoc institution). First, this helped a lot with networking. Second, and perhaps more important, all this experience gave me a ton of confidence in my ability to give good talks. That confidence spilled over into the rest of my interviews, which was generally a very good thing. I didn't really start giving many talks until during my postdoc, but in retrospect, I wish I'd given many more in grad school.
All grad students know that if you want a job in academia you should publish lots of good papers. But many of them don't grasp the value of learning to communicate clearly and to publicize their work. During my postdoc, I set aside 2 or 3 weeks to learn how to draw good pictures to go into my talks, and I think that skill has really improved their subsequent quality. Personally, I do everything using beamer and tikz (presentation packages for latex). However, your specific tool is not so important. Ask around and find a tool that is widely used and supported by folks in your research area, then invest the time to learn to use it well.
The second really important thing you can do is network. When I was in grad school, I had no concept of how important networking is for a career in academia (in fact, almost any job). Many of my papers have grown out of conversations that started at a conference. Once people know you, they invite you to speak (at their school or at a conference session they're organizing). As you get to know more of the key researchers in your area, you find it easier to keep up with important new developments (which better inform your research, etc.).
Do awesome research.
Get famous people to rave about it.
Everything else is noise.
I'm in your field, and I'm a bit later in the game than you are, as I completed my PhD in 2010. Here's some advice, in increasing order of importance.
A very good way to get a feel for what it takes to land faculty positions is to take a look at the departments you would like to work at in the future and scope out the Assistant Professors. Many of them will have their CVs and Teaching and Research Statements updated to when they applied for the position.
You will need to cultivate several strong letters of reference, hopefully by working with some of the bigger names in your field.
Try to go to a few job talks, as this will also give you a sense of what a strong research agenda looks like, both in terms of accomplished work and future directions.
You will need some teaching experience, but being a great classroom teacher will not get you a job if your research portfolio is weak unless you are going to a school that focuses on undergraduate education.
Computational Science is a bit of a funny field, as we live at the intersection of several very different fields: physics, mathematics, computer science, and usually some scientific application. These fields all have their own rules for hiring and promotion, and this is important to understand, because you will almost certainly land in a department that is not titled Computational Science.
You need to statistically look good, because the members of the hiring committee will have almost no other grounds for justification besides what is written in your hiring application. This means you will absolutely need a good number of high-quality journal publications, preferably at least 5, when you apply for a faculty position. Conference papers only count for a Computer Science department, and you may need twice as many to be considered in that direction.