If there's one thing that we fail to do in science, it's give people any real indication of what's involved in their 'next step' in the field. When I was an undergrad signing up to do an 'honours'1 major, I had no idea what an honours project actually entailed. While I had to declare my major during my second year (or 'sophomore' as they say here), it wasn't until the end of my third that we had a meeting to explain the project. Similarly, I had no idea what being a grad student was like before I began doing my M.Sc. During my Ph.D., the impression I got of postdoc-ing was something along the lines of: 'Work like crazy until you become eccentric if not insane'. Thankfully, while postdoc-ing is certainly a lot of work, for most people, it's not quite that bad.
Anyways, whether you're going to grad school or a postdoc, chances are that you'll be applying at multiple locations, possibly going for several interviews. One thing to keep in mind is that these aren't like the job interviews that we've all become accustomed to during our high-school years and summer breaks. Starting with grad school, but especially in the case of a postdoc, these interviews should be much more reciprocal: The lab needs to determine whether you're a good candidate while you need to determine whether the lab will be an appropriate fit for your objectives. So here's a few pointers that I've gleaned both in my experiences going on interviews, but also being involved in interviewing candidates.
 
1. Know what the prospective lab does.
I'm sure that this strikes most people as obvious, but you'd be surprised. You need to go back and read the last few years worth of papers that came out of the lab and be ready to discuss their contents with your prospective PI. This takes time and work and it's why I disagree with people who send out blanket applications to a bunch of labs. Obviously you want to go to a lab that will allow you to pursue your own interests and it's probably best to restrict your applications to those labs that actually interest you. Finally, it's also helps to cater your talk (yes, you'll have to give a talk) to the group's interests; however, always put sufficient background into the presentation such that it could appeal to anyone.
2. Know your stuff.
A postdoc should be an independent researcher. You shouldn't need someone to tell you what to do next, or how to design a research project - you should've learned this during your Ph.D. When you show up at a lab, you should have ideas about projects that you could carry out in that group (even if you're applying for a position with a pre-determined project). Even if you haven't defended your Ph.D. yet, you should treat the time that you're interviewing as a defense of sorts: You need to know your current project inside-out because people are going to ask you questions about it. I've never been to, or been involved in an interview where I or the candidate was not asked 'what could you see yourself doing in my lab?' I wouldn't answer that with 'I don't know' or 'I'll think about it'.
3. Ask 'tough' questions and pay attention to what people say.
Here's where that reciprocal interview aspect comes in: You want to know what it's like working in this lab. Take it from someone whose seen several different 'lab management styles': the way that things are run can vary wildly and you may be more comfortable with certain styles. You want to ask many questions of both the PI and the lab members - preferably each alone and in a group. There are the basics: You'll want to know how the lab's doing in terms of funding: will you be able to carry out the projects you want to do? What about conferences: does the PI send postdocs to a yearly meeting? How about manuscripts: does the PI allow their students/postdocs to write their own papers? Does the PI have any particular view on publications in general? (we all want Nature papers, but if you won't be allowed to publish any manuscript that doesn't go to an impact factor 15+ journal, that may be a problem2). Have postdocs in the lab generally gone on to successful careers? If so, what have they done (academia, industry, left science altogether, etc.)? What about projects? Does everyone in the lab get their own, independent project or are you going to be competing for the same prize?
The above are all of the kinds of things that you can ask both the PI and the lab members, but there are a series of questions that you should reserve for lab members themselves. Things like: What's it like to work in this lab? Does the PI expect you to work 14 hours a day? Is the PI respectful and do people feel as though they're able to voice concerns about projects based on their expertise? How's the lab dynamic? Do people get along and work together? How about the department? Are there a lot of collaborations going on between labs? Are there people for you to talk to about your work in terms of 'outside knowlege' (e.g., statistics or computational help? What about living in the area? Is it nice, are there things to do, areas to avoid, etc.?
Pay attention to both what people say and what they don't say. Are people being cagey about their comments or dancing around issues? Are some people in the process of leaving, and if so why? Are you meeting with everyone in the lab or only a subset? If the latter, why? Are there people that the PI doesn't want you to talk to? It's a much better sign when the PI wants you to meet and talk to everyone rather than a set number of folks.
At the end of the day, you need to take all of the answers that you get and weigh the pros and cons. There are always going to be issues - no environment is perfect and the nicest, best PI in the world is occasionally going to have disagreements with some lab members. People saying this or that particular negative thing should be taken in context: Ask yourself if it's going to be a problem in terms of your potential experiences in the lab. I think that a lot of people assume that the purpose of these interviews is 'all business' and that they should stick to questions about the science itself. Remember though that you actually have to live there: will doing the best project that you can imagine in a lab where people don't get along and in a place where there's nothing to do be okay for you? For some very particular, focused, and motivated people, that's fine. I doubt that it's the norm, however.
4. Think about what you want to accomplish during your postdoc.  
To me, one of the most frustrating aspects of post-secondary education is the the strange 'next-logical step' attitude that many people take. Fine, you're going to college because everyone else is, but doing a master's degree because you don't know what you want to do is kind of overkill isn't it? Surprisingly, some folks seem to make it all the way up the ranks to a postdoc using this same sort of logic. To be clear: I'm not talking about people who are wondering whether they should be pursuing a career in academia vs. one in industry: that's typical of anyone at the professional level, and with a few exceptions, your postdoc will probably contribute positively to your job prospects3.
I don't think that anyone should be doing a graduate degree unless they really like what they're doing. I've had a surprising number of direct interactions with people who were in grad school 'while they decided what to do next', and it was a major drag. Unfortunately, a lab is like an organism unto itself - there's a lot of shared tasks, exchanges of ideas, and co-worker support involved. When one someone's not picking up the slack, it can make things very difficult.
In my experience in academic labs, the postdocs are typically the hardest workers, and the ones that grad students turn to when they have questions. Being more independent means more responsibility, so think about this before you sign on to a contract.
In terms of what you want to accomplish, the advice that I've received is that you should use your postdoc to build the kind of research portfolio that you will be able to translate into the kind of research that you're going to want to do in your own lab. You don't want to spend all of your time doing random busywork, or working on unrelated projects just to get your name on papers. Are you going to be able to carry out the kind of project that will get you recognition such that fellow scientists think of you when they think of your field? That's quite daunting to contemplate, I know, but I suppose that that's the sort of thing that you have to think of at this point.
 
So there you go, a few ideas that I hope will serve someone well when they go out there and take the next step for themselves. Do the background work to know exactly where you're going and ask the right questions. If your lucky, you'll be in a situation where the difficulty in your choice involves deciding between which awesome lab you want to go to! If anyone has any other pieces of advice (or comments on mine) feel free to leave comments and I'll add them to the post.
 
1I have a policy of using American spelling for everything that I write. This is entirely for practical purposes: American scientific journals often require American spelling, while non-US publishers accept American or British. However, in this case, the major was done in Canada, so British spelling it is!
2As crazy as this may sound to some people (especially if you come from a basic biology lab like me) this happens. I know of multiple cases, so these are the kinds of things that you want to find out about.
3The 'exceptions' would be situations such as one that a friend described to me: Having done a long postdoc makes you 'more experienced' and thus 'more expensive in terms of hiring' for some industry jobs. Depending on the job, I guess that they may want cheaper, fresh-faced Ph.D.s?