Getting a university teaching job is a very difficult undertaking. It's hardest in the humanities and social sciences, but is slightly easier in the hard sciences. At present, there is a glut of Ph.Ds, and therefore, universities average between 100 and 500 applications per job. Since many of the applicants are already experienced university professors (sometimes with tenure), getting a job right out of graduate school is very difficult. The best way to improve your chances of being hired is to make certain that the job you are applying for is exactly in your field of expertise.
Complete your Ph.D. first. It is very difficult to finish a dissertation while putting your career together in your first year at an academic job. ABD (All But Dissertation) applicants are often disliked among university hiring committees for this reason. In addition, university hiring committees also want to make certain your dissertation is defended and accepted before committing.
Never apply for a job that is not precisely in your field of expertise. If you have a Ph.D. in Russian studies, do not apply for a job that demands a degree in Ukrainian studies--these are close, but not identical. There is too much competition for this to be a successful strategy. Most search committees will look at your areas of expertise, and if they are not an exact match for the opening, will consider you no further.
Try to get a recommendation from at least one major name in your field. This might seem superficial, but university hiring committees like celebrities. It is often the case that the "weight" of an applicant's letters of recommendation becomes the deciding factor for who eventually gets hired. Dropping a few names during the actual interview might help a bit. If you have no "names" on your list, make certain to speak about your doctoral committee members' publications and books. Chances are eventually, you will hit one that the hiring committee will recognize. Do not underestimate how important this name or publication recognition is in the hiring process.
Avoid PowerPoint presentations or other gimmicks at your job talk. The job talk is to show the faculty and other people on the committee that you are a good speaker, can convey complex information, and can field questions in a professional manner. You will be interviewed both in a one-on-one and a group setting with many members of the department and administration. The job talk is a lecture, and will likely be to the entire department. Focus on your knowledge, not on showy presentations.
Do not worry about your prior teaching evaluations while visiting an interested university. Most departments won't give these much weight, and it is unlikely that an applicant would submit negative evaluations from grad student teaching. Do, however, bring copies of your syllabi to your interview and job talk. That is something that most departments care about.
Be as sociable as possible while going out to eat with your prospective colleagues. The "dinner" is an old tradition in the university hiring process and is very important. Take it very seriously. Do not order alcohol. Behave appropriately. You will not be asked questions of academic value--this is a test for your personal "fit" in the department. While often not spoken about, one's ability to "fit in" with a department is far more significant than your actual teaching ability. Show that you can roll with the punches, have a good sense of humor and do not intellectually threaten the rest of the department. This may well be the difference between a good and a bad experience. Many professors will vote on a candidate based on whether or not he will fit in. It is often assumed that the candidate is competent in his or her field and such questions are rarely even brought up in the hiring process.
Seek out the dean or assistant dean of academics. These positions are experiencing a tremendous expansion of their power. A word from them can make all the difference. Therefore, it might be just as important to impress them as the tenured members of the department