Good ways to multitask
I have three answers to this question; I'll put them all here for you.


Don't.

Multi-tasking is a necessity when there are many tasks that demand your attention all at once. The people who most need these skills are either managers, whose work demands that they divide their attention among their subordinates as necessary, and those working in a highly collaborative environment, where interaction with colleagues happens regularly. 

As a graduate student, this will almost never happen. Your responsibilities will typically include coursework, teaching assistantships, and research duties, and writing. Even your collaborations will happen at a slow pace. You'll rarely be in a situation where you need to get in touch with someone within the hour; almost all your issues will be able to wait a day. Considering that almost all research shows that multitasking decreases productivity, consider yourself lucky.

To that end, if you can train yourself to focus on a single task at a time, your work will benefit from it. 
Pomodoro technique

I recently (~6 mos) read about this technique online, and I've found it very useful for certain tasks. The concept is ridiculously simple. Before you start working, write down the task you're about to start on a piece of paper. Start a 25 minute timer and work until it runs out. Take a 5 min stretch, put a tic next to the task on the piece of paper, and then repeat until you're done. If you need to switch to something else, write it down on the paper as well, and switch every 25 minutes. This way, you always have at least 25 minutes to do each task, and you can set up your multitasking in 25 minute chunks. (As an added benefit, you're taking stretch breaks every 5 minutes, which is good for your health.)
Getting Things Done

There's an answer below that mentions this, but doesn't do it justice. I've been using this for years and it's a wonderful way of keeping track of what you need to do. At it's simplest, the technique just advocates that you make a to-do list of everything you need to do. The useful part of this technique is how he separates tasks; he puts them into "contexts", which you can think of as "environments". Some tasks will be done at home, some at work, some wherever you have email access, etc. By breaking up tasks like this, you can easily see what you need to do at any given time by simply consulting the correct list.

This technique has gained immense popularity, and because of that many to-do lists online feature "GTD compatibility". This basically means that they let you make lists of your to-dos.

This method comes with a catch; if you don't do it rigorously, you may as well not do it at all. As soon as some tasks aren't on your lists, then you'll stop checking the lists, and then the whole thing goes to pot. However, if you keep the lists current, then it's an immensely helpful technique. For forgetful people like me, the to-do concept is a veritable necessity, and the context idea is a good way of segmenting what you need to do.