I've been getting quite a few queries from you lately with regard to if/how to follow up after an event / fair / company presentation if you got 1 or more business cards from people that you would like to leverage to increase the chances of getting an interview.
Are you prepared for no response?
The biggest point to realise up front with a follow-up email or conversation is that in 95% of cases, it will appear to you are if nothing came of it. By this, I mean it is extremely rare that someone will respond and say "yes, it was great to meet you and I'll make sure we get you in for an interview". They need to be seen to follow due process and also don't want to set a precedent that that is the way to get an interview.
You might never know if your email had any impact on you getting an interview. I know countless grads that have gotten interviews (or sometimes even internships or work experience) based on someone they met who really liked them, but they will never know how hard that person worked 'behind the scenes' to make sure they got the opportunity.
So, be prepared for the unknown - I flag this upfront only because I know a lot of grads tend to be very disappointed if they hear nothing back and either send another email (which can start to look too eager) or get very disillusioned with the company.
What media to use?
I strongly recommend email. Whilst some students opt for a formal thank you letter in the mail, and it possibly does 'look' better, the problem is that paper is so rarely used now in grad recruitment that the chances of it getting lost/filed away is high. Unfortunately its unlikely someone will go to the effort of scanning it in. Equally phone calls, whilst personal and usually quite amiable, area easily forgotten and are not recorded. An email can be easily forwarded, file, revisited, uploaded to a recruitment system or attached to a candidate record. In my opinion, it is definitely the way to go.
The follow-up content
It is absolutely worth doing a follow-up if you got someone's details. Many people will do something with an email they get - e.g. pass it onto recruiters or colleagues, etc.
The content of your email should be dependent on three factors:
1- who they are and what their role is
2- how you left things with them at the event
3- what your next steps are / have been
Typically the 'who' will be either a recruiter/HR person, someone from the business, or one of the previous years grads.
If your card is from someone in the business / in a line role / manager level, then you need to write a concise, solid email - nothing too long or they will just take one look at it and decide they don't have time to read it. Figure out what you want to say - is it a thank you, is it to express interest in their particular area or team, is it to ask a further question? I would urge you to keep it to no more than 1-2 short paragraphs. Try to link to the conversation that you had so that they might remember who you were and the conversation you had. If it's your intention to apply, or you have already applied, then I wuld let them know. And in some cases, if you're feeling that you got along very well with them you could potentially attach your CV. I would not even make reference to it, but maybe just sneakily attach it on the end regardless on the off chance they open it.
If your card is for a recruiter, again, I would make reference to the conversation you had. If you want to get on their good side, perhaps offer some feedback on the parts of the event that you found particularly useful. If the purpose is a thank you, then I would keep it fairly short. If you have further questions, then I would ask them (but make sure the answers are not already on the website or in the brochure). Let them know if you have applied / intend to apply and to which programme/internship/role.
If your follow-up was with former grads, then you should ask them for any more info you need fairly openly. They are usually pretty quick to help applicants as they were in the same position a year or two before. They are least likely to try to pass it onto HR to influence the process though - just something to be aware of.
If you did leave the conversation with someone a certain way - a promise to send a CV, a link, have a call about something, etc, then make sure you do so within 1-2 days of the event, otherwise they will have moved onto the next Uni and you will have faded in their memory - they are often meeting hundreds of students a day.
Behind the Scenes
There is usually some sort of follow-up activity after most events - conversations between the business and HR about candidates met that they would like to keep an eye for applications from, etc. However, from there everyone usually goes through exactly the same process as everyone else - so once you've leveraged the follow-up once to get the interview, I wouldn't try to use it again to 'guarantee' yourself the job. It won't work and it will only look like you are trying to get in through a backdoor because you are not confident enough you will make it through the interviews.
So, in summary, it is definitely worth doing a thoughtful follow up soon after the event if you have a name. And to be honest, even if you dont have a name, it might be wort a short thank you to a generic grad recruitment address. People are only human and after a long day / night talking to grads (and countless weeks before planning it), everyone appreciates a thank you and you never know how it might help you behind the scenes. Sometimes, you can make your own luck...