The jumper cables are not for changing the tire but for charging the battery if it goes dead. You need another car or a special battery to use jumper cables (i.e. you need a charge from somewhere). AAA, if you can afford it, is also quite useful as they will come and do these things for you free of charge provided you can get a hold of them (hence cell phone).
If your advisor gives you a project to work on that is supposed to be new research, ask what are the most relevant papers in the literature an do a literature search yourself to determine the state of the art for your problem. Go and discuss the other papers with your advisor so you get their perspective on the literature. Since there is a vast literature out there, this means that you need to learn to read papers for overall content without going through all the details. Then pick and choose which ones require a more detailed reading.
Make sure you do not overlook the literature that is not in print online, some excellent and relevant papers published just 10-15 years ago are not online and require you to physically walk to the library and read the papers in the journal (or make a photocopy and bring it back). I have seen manuscripts written by younger authors rejected because they duplicated material that was published in the older printed literature.
When I wrote my PhD thesis, latex had just been invented an essentially none of the journals were publishing online (the internet was in its infancy and had not yet gone commercial). So I know how it is to go to the library and photocopy. It's not all that time consuming if you do it efficiently and copy several articles at once. I have one paper that needed a sharp estimate from a paper of Nagy written in the first half of the 20th century. We had to go to the library and look it up in print. But this prior paper allowed us to prove a sharp estimate in our work that matched results from asymptotics and simulation. I can not stress how important it is to take into consideration the full scientific literature when writing your own research papers.
Another reason to follow the scientific literature is that it gives you a broader perspective about what has been done and what are the active areas of research. You will have to pick your own problems at some point in time and you will need to know this by that time.
Everyone should practice their first lecture by writing it out on a board and then going to the back of the room and seeing what it looks like. Correct your presentation until it looks really good from the back of the room. Next, make sure that if you expect the audience (e.g. students) to take notes, that you write at a pace they can keep up with. There is a sure-fire way to gauge pace. After you write a paragraph on the board, look at the audience and stop talking/writing until most of them have finished taking notes. Then continue. The silence is a lot shorter than you might think. Make sure you write everything you want in their notes, on the board. A Typical student will copy what you write and not embellish, even if you say more than what you actually write. This can be tiring for your arm but it is necessary if you want to deliver a good blackboard lecture. In addition bring a friend to listen to your delivery and see if they can hear you from the back of the room. If you aim for the back of the room when you lecture, everyone in between should be able to hear and see you. If you aim for the front, you will almost surely miss the people in the back. If you have trouble speaking loudly, consider getting a voice coach (just temporarily) or practice breathing deeply to your diaphram and pushing with your stomach and back muscles when you talk. It may feel like yelling but remember that you are a performer when you give a lecture. You are not having an intimate conversation with the person in the front. Therefore, act like a peformer and speak to the back of the room as if you were acting in a play. If you have ever sung in a choir it is similar only speaking instead of singing. Asking questions is also good and keep the whole group in mind when you do so. There is an aspect to giving public lectures that has elements of improvisational acting. If you have done that you should be great at giving lectures. If not (and most of us have not, myself included), after giving a number of lectures you will get more comfortable talking off the top of your head in front of a crowd and having them enjoy the experience. For the most part, they are there to learn and are expecting to enjoy the experience so if you don't do anything to shatter that expectation, you will do just fine (i.e. it is the `innocent until proven guilty' rule that applies to university teaching, unlike some other types of teaching). This last idea is important to keep in mind if you tend towards stage fright.
If you do not teach and tend towards stage fright and have to give a presentation, then consider powerpoint, see above, as it gives you some physical material to hide behind and saves the problem of writing well on the chalk board.
When delivering a research lecture at the board, you can take some liberties with the above (in particular the note taking) but it should be only so that you can deliver additional information to the group. Moreover, the `back of the room' rule still applies.
Perhaps most importantly, always try to guage the knowledge level of your audience when giving a lecture. You want them to walk away with new information that connects well to what they already know. This rule applies whether giving a calculus lecture or a research colloquium.