I have now reached the proper age to give advice! As some of you know I have had the pleasure of having mentored or co-mentored nearly 50 postdoctoral fellows. I thought I would share some thoughts on this matter.
To start with, mentoring has, in spirit, the dynamics in making a friend. Not all combinations of people can become good friends. Ditto for mentoring. Of course, as a mentor you will be able to stand a larger dynamic friend, relative to that appropriate for friendship. However, there are clear limits to incompatibility that you should be aware of.
Next, never never take upon a post-doc unless the person is very good or has some special talent. This is true even if they come for "free" (i.e. a Hubble fellowship, a fellowship from their country etc). Do not assume that just because they have been selected by a prestigious panel they are suited to you.
I realize that young faculty are frequently tempted to take upon "a warm body and a pair of fresh hands". There is a perpetual need to flat field data or build a few tools for you numerical analysis package.
Mentoring takes time and you should conserve your time and aim for an exquisite track record, whence the above admonishments.
Here is what I have been doing in terms of identifying interesting young people:
[1] I am always on the look out for interesting young people (either by asking colleagues at meetings or via talks at conferences and especially workshops). I then get a confirmation from another colleague (sometime some professors push their own students).
[2] Invite students (usually those in the fourth year) for a visit. I set aside funds with a clear cap (e.g. $400 if from West coast, $600 if from elsewhere in the US and $800 if from Europe; I suggest that they ask their advisor for expenses over this amount). If the student's research is aligned with one of my grants I pay for it (my strong preference). For theory students I usually request Sterl for Moore funds. For radio astronomy funds from OVRO etc. Sometimes the EO is also a source of funding (especially if the person is a prospective faculty hire).
[3] In advance of the visit I circulate the CV of the student (along with a summary of my view) to relevant faculty.
[4] I designate one of my students or postdocs to be the host (explain ground transportation, help find local accommodation, arrange desk, seek appointments with faculty, keeper of schedule, and arranging a talk).
[5] I make a point to spend some time with the student. About half the time (or more) I find the student not as interesting as advertised. When I do find an interesting student I then encourage them to apply for a post-doc at Caltech (either national fellowships or Institutional fellowships).
The same approach is used for first time post-docs (though my strong preference has been for graduate students). Here the motivation is to identify prospective faculty candidates.
Sincerely
Shri