Just some advice as we are getting a bit closer to intern season. Hopefully people will start adding more in the comments, I wanted to stay away from the obvious ones.
The Do Not's
1) Do not screw up a lunch order: I know, this is quite obvious, but I can't stress enough the importance of this. A key trait that is looked for is reliability. Until you are trusted you will not even get to do a booking unsupervised. And trust is built up slowly through increasing stages. First stage is menial tasks like food delivery or in general stuff that isn't actually related to the business and therefore the max downside is inconvenience for the trader.
Next comes things that are to do with the business but do not affect pnl i.e. bookings and spreadsheets. Next step is simple hedging tasks and cash product execution. This is a big step as at this point you can affect pnl. Specifics differ by desk, but for example on a flow derivs desk this includeshedging intraday and on the close, and hedging the rho of the books. After that comes some responsibility for pricing under supervision, then pricing unsupervised, and finally sole management of a book. But it all begins with the lunch order.
2) Do not ask simple questions: everyone always says there is no such thing as a stupid question. Maybe that's true, but there is such a thing as a simple question. A simple question is one that can be googled. For example you are on an options desk, don't start asking about simple characteristics of call and put options (i.e. whats the div or interest rate risk), these things can be easily learnt in 2 mins. What you want is to know things like this that can be easily researched and then use that knowledge to actually ask smarter questions.
When you learnt the basic knowledge yourself you can actually have a discussion with the traders on how they run their books, for example what kind of div risk he is running, how he is hedging/managing it. From a traders perspective you will get a lot more points from a 30 min discussion about the persons book than being taught basic things you should have already learnt.
3) Do not think you can get involved with office banter that is about the people on the desk or anything/anyone in the office: this is a classic mistake. Especially in the current environment there is a lot of "gallows" humour regarding the state of a company, bonuses, firings etc. I have seen interns try to get involved and crack jokes and it never gets taken well. As an intern you are not an "insider", so don't pretend to be one of the guys. Now this does not mean to not get involved with general banter, just don't try to be part of inside jokes where its actually disrespectful on your part. Gallow humor is only available for people in the situation.
4) Do not at any point come in last on the desk, even after a night out: Doesn't have to explained, be the first one in. After a couple months working you will get the hang of things but as an intern and grad you want to get in early and make sure you are up to speed with everything.
5) Do not wear your extremely expensive watch until you are 100% sure it won't be an issue: even if it rubs one person the wrong way it's not worth it.
6) Do not take a seat at any meeting table until you are sure every person more senior than you has one: This one makes me laugh, if you have a morning meeting and theres a table, don't go in thinking you will sit down. Any chair is for senior people, interns stand.
1) Make it your mission to talk to as many people as possible: My first rotation was on a sales desk that really didn't interest me, and the project I was set was hugely out of my comfort zone. I was ordered to sit with every desk on the floor. Turns out this might have been the key for me to getting hired. By the end of the three week rotation I had sat with almost every area of the floor, which a) helped me get exposure, at a lot of places the hiring process is almost like a vote so you want as many MDs to know you as possible and b) really helped me find the desk I fit in the best, and then allowed me to network to make sure I got a rotation on the desk I wanted.
2) Whatever you get taught during the day, review your notes before the next day and make sure you can answer questions on the topic: One of the things you are judged most on is how you pick up information. If you learn something, you should be able to answer questions on that stuff from then on. Its not university where you have an exam at the end and you just need to learn it before the day, but you need to be able to absorb information like a sponge. If a trader teaches you something, 10 minutes later you should be able to answer questions on the material.
3) Always act humble: general life advice, but the second you get cocky people will want to try and knock you down a peg if you are an intern.