Congratulations on landing your first interview!
Let's go step-by-step: think of this as your checklist.
Part I: Confirmation
Make sure to know when, where and who you will be meeting. Research your interviewers beforehand to see if you have anything in common, which you may use during the interview to break the ice. Have the contact number ready in case you are running late.
Part II: Dress code
Advisory firms have a strict dress code of suit and tie for men, pants or skirts at the knee for women. So guys, please: dark blue or grey suit; dark shoes; no flashy ties, shirts or socks. And girls, please: avoid showing too much cleavage or wearing ultra-high heels; this will be noted (and not in your favor).
Part III: Timing of arrival
Reaching the interview venue 10 minutes early gives a positive impression. Arriving too early will have you waiting a long time, and will make you more nervous than you should be. Worst of all, you may actually risk pissing off your interviewer, who already has other, more important things to do. Arriving late without notifying the interviewer is unforgivable.
Part IV: Handshake (post-Covid)
Your handshake should be firm, but not crushing. There is nothing worse than a wet or weak handshake: people never forget either, and will hold it against you.
Part V: Introduction
During the first 10 minutes, your interviewer(s) - typically one or two among the team's assistant managers, managers and directors - will provide an overview of the organization, the team structure and the specific role for which you are interviewing. Make sure to bring a notebook and take notes: it will be helpful to reread them after your interview (when you are less nervous); it also gives the impression that you are interested in what the interviewers have to say.
Part VI: Tell us about yourself
At the end of the introduction, the interviewer will utter the famous sentence: “now tell us a little about yourself”. You now have the floor. The next 15-20 minutes will be dedicated to your background, education and work experience. The key is to start from the end: begin by telling the end of your story, i.e. talk about your current role or the university program you are attending, and then work backwards. The interviewers most likely couldn't care less about where you were born and what you did in the 18 years after that, even if you think you may have a particularly exotic story to tell. Even if they seem chill, never forget that this is a professional setting and they will be noting and judging your every word and action. You’ll have plenty of time to share your life stories once you're in. But at this stage, keep your eyes on the ball. They will let you talk, saving their questions until after you are done, but don't take advantage of this by blabbing on for longer than 20 minutes (it will be counterproductive).
You can be sure that the interviewers will want to investigate suspicious gaps in your professional experience, or a longer-than-average duration of your studies: questions like “did you take a break between the years x and y?”, or “it seems like it took you 1 extra year to complete your masters degree, why is that?” will come up 99% of the times. Remember: you are interviewing with people that love to drown their clients in questions. Before you even step into the room, you need to be aware of any "weakness" present in your resume, and have a valid (and believable) explanation for it.
Part VII: Grilling
Just like that, your first 30 minutes are gone. And now it's time for the interviewers to have their fun: over the next 30 minutes (or less, depending on whether they liked your introduction or your answers during the "grilling"), they will try to put you to the test to see how you react, whether you close up or shine. They will do this in the following ways:
Math problems, puzzles and brain teasers - you may not believe it, but there are people in this world who like to do puzzles in their free time. Some literally get off on solving riddles. And they cannot wait to test other human beings, even when on a date (true story). So make sure to brush up on the "9 balls and a scale", "angle between the clock hands at 3:15", "98 x 52", "how much does an aircraft weigh" and "how many gas stations are there in Italy" kind of puzzles. Remember: the interviewers are not interested in hearing the right answer come of our your mouth (although it helps if you get it right, really), but they want to test your problem solving skills, see how you handle being faced with a problem and your individual way of getting to the solution. In other words, they want to see how (and if) you think.
Technical skills - unless you cried or insulted the interviewer while trying to solve the brain teaser(s), you will not be too penalized by an eventual subpar performance in that part of the interview. The interviewers are much more interested in checking whether you know what you're doing and/or paid attention in class. During this first interview, they may do so by asking you high-level questions on how you estimate the beta, what discount rates to use to discount FCFEs and how the DCF works. The real examination happens during the second round of interviews.
Language skills: always (and we mean always) be honest about your level of proficiency on all skills included in your CV, but especially on the languages you speak. Before identifying yourself as native or fluent, think of what would happen if a truly native or fluent speaker were sitting at the other side of the table during the interview. You guessed it: it would not end well for you. Lose credibility on one section of your resume, and you will lose credibility. And this may be the easiest way for interviewers to check your credibility. Don't give them an easy excuse to turn you down: make them work for it, at least.
Part VIII: Questions
The interview is coming to an end. No matter how your interview went so far, your interviewers will always ask if you have any questions. Just as for the irregularities in your CV (if any), come prepared with a list of relevant questions, maybe already written on your notebook. Avoid blankly saying "no": that will make you look uninterested, and probably a little dumb. Here's a list of questions you should ask (unless they have already been answered by your interviewers during their introduction):
Are you hiring to expand the team or replace someone who left?
What is the typical turnover rate of the team?
What is the typical career path at the firm?
What are the training programs offered by the firm?
Does the firm pay for certifications?
Who are your biggest clients, and what kind of projects do you do for them?
What is the typical duration of a project?
What are the typical working hours?
What skills and qualifications are expected of the person holding the role in question?
What is the most challenging aspect of the job?
What are the timelines and next steps of the interview process?
Is there anything else you would like to ask me?
Whatever you do, never, ever talk money during the first interview. Also, remember that you do not have to disclose how much you currently earn to anyone (but if you do, inflate).
Part IX: Thank you email
The day after your interview, it is good practice to send an email to thank your interviewers for taking the time to meet with you.
For questions or clarifications, feel free to reach out. Thanks for reading, and good luck!