Job interviews are like chess matches. Both of you are trying to get a feel for each other, and you’re trying to make enough of a good impression to win the battle. Getting a second interview is your first victory. Having a second interview means they’re interested. That also means you’ll really have the chance to sell yourself, and guarantee you’ll get the job.
The second interview is less about checking your qualifications, and more about seeing if you’re the right fit for the job. You’ve already been confirmed as a good candidate by making it this far. In the second interview you’ll face tougher, and more involved questions. The best way to handle these is to stay true to yourself. Be the same person you were in the first interview.
The worst strategy you could have is to try and handle the interview differently. You’ve gotten a second interview because the interviewer saw something in you. Don’t cover that up by being a different person, or else you won’t make the best impression. Instead be the polite, confident, and assured person that showed up the first time around.
Whatever research you’ve done about the company before, go over it again. Know your stuff as well as possible, because the questions are going to be tougher. Only by having the information can you respond to the best of your ability. Quick concise responses are key here, showing your comfort and ability just by talking.
Make sure to show how you can contribute to the company, and compliment them on aspects you appreciate. There’s reason you want this job, besides the paycheck. Find that and play off of those reasons. Make your skill set work for what you want from the company. That makes you into an ideal employee, and helps you shine in your second interview.