I am a PhD student right now, and I'm looking towards doing a post-doc in the future. There is a research laboratory where I want to do my post doc, primarily because there are scientists engaged in very similar topics to my dissertation work. I've never met any of them personally, and I know that the standard approach is to network with them at conferences first. Someone had suggested to me that it is possible to target an individual in that institution, and somehow invite yourself to their lab to meet them, potentially giving an unofficial (non-departmental) talk in their lab. I know that this is not a standard approach, and I think that if I'm not careful I might give a bad impression in the process. How can I invite myself to the lab if I don't have a personal connection to a researcher in that institution?
One thing that sometimes works is the following:
While this is a little passive-aggressive, I've found that more often than not, they'll ask you to give a talk, and even if not, you might get a chance to meet with the lab folks, which is the real purpose in any case. Make sure that the PI is around though.
I'm also doing a PhD and have a 'target institution' for a post-doc. I visited it already, but my supervisor knew the guy there and he made first contact.
I got the impression that it's common practice to have people from other labs just visit, and that the stuff you can do while there is entirely flexible. My visit (two weeks) consisted of me sitting at a computer surrounded by local lab members, doing my own work, and talking to all of them about their work during lunch breaks. I also arranged to do a joint experiment with the PI there, which will now become part of my PhD, and we roughly agreed on a research design while I was there. I didn't mention the post-doc idea yet, as I think it's best if I prove my worth through this joint experiment first.
On the first day there, I was asked if I would give a talk (which I did). I could even choose how big an audience would be invited.
While visiting, I also discovered another lab at the same university, which does related stuff to mine. I just e-mailed them, saying I'm in town (from lab so-and-so) and asking if I could come talk to them a bit. I googled their web page and came up with a few names of people I told them I'd like to talk to, although I didn't know much about any of their work. I did not ask to talk to the big names, in that lab, just PhD students and post-docs. What did they do? They immediately asked me to give a talk (which I did).
Overall, my impression is that this is standard practice. People like to hear about related work. I would suggest that you just e-mail someone there, tell them you find their stuff interesting (it's best to mention some specific result of theirs, so that they see you're really into it), tell them you're working on something similar and ask whether you could visit their lab. I would guess that you'll end up giving a talk. You can also suggest it yourself, once you've established communication and exchanged a few e-mails.
It seems like you are worried about it, so you might want to ask your advisor to do the intro. PIs generally appreciate getting a a heads-up on good potential postdocs.
I think it would make a better impression if you were comfortable to do it yourself. I would start off pretty light by sending the PI an electronic "reprint" of something related to a conference you attended/are attending. Something like: "I was hoping to meet you at the basket weaving conference, but I didn't see you. I have attached my poster/talk/reprint." This works for either a recent past conference or an upcoming conference. For an upcoming conference, if they have an abstract tailor the email appropriately.
Hopefully the PI responds, but if not, then go a little harder. Send them your CV and tell them you are looking for a post doc.