How should I cite something learned second-hand (eg, from Wikipedia) when I haven't seen the primary source? I want to cite something that I have learned from a Wikipedia page. However, I'm loathe to cite Wikipedia because of the perception of it by my tutors, so I try to cite the original source.

What should be the correct thing to do when I'm unable to have sight of the primary source myself, or find it in a collection (for clarity, I should add that I have the details of the source - I just can't find it in collections available to me)? Should I just cite as much original information as I can, or should I defer to citing Wikipedia? I'm hesitant to do that, because a glance at the citation would suggest that I was 'too lazy' to source original material or just dig deeper.

For additional clarity - I know that citing Wikipedia is 'bad' etc.  The emphasis is on how to cite something that has been learned via Wikipedia (as an example) but for which the original material cannot be seen or retrieved from available collections or searches.
What you're referring to is an indirect source. In general, you should always work as hard as you can to find the original source. If that is not possible, all of the major style guides include a way to cite indirect sources. Note that you should not cite Wikipedia (see the "do not cite Wikipeida" note at the end of this answer). If an indirect citation is absolutely necessary, it should come from a reputable, peer-reviewed journal or other academically respected source.


According to Purdue University, the MLA rule is to name the author of the indirect source in the text and cite the work you have in-hand:


  For such indirect quotations, use "qtd. in" to indicate the source you actually consulted. For example:
  
  
    Ravitch argues that high schools are pressured to act as "social service centers, and they don't do that well" (qtd. in Weisman 259).
  
  
  Note that, in most cases, a responsible researcher will attempt to find the original source...


Williams College further clarifies that the indirect work should be included in your Works Cited list:


  ...include the indirect source in the Works Cited.

The APA rule (also from Purdue University) is to exclude the indirect source (called the "original source", below) from your reference list and only include the work you have in-hand (called the "secondary source"):


  ...name the original source in your signal phrase. List the secondary source in your reference list and include the secondary source in the parentheses.
  
  
    Johnson argued that...(as cited in Smith, 2003, p. 102).
  
  
  [...] Also, try to locate the original material and cite the original source.

The Chicago rule (once again, from Purdue) is to cite the indirect source, followed by the in-hand resource:


  ...Chicago discourages the use of [indirect sources]. In the case that an original source is utterly unavailable, however, Chicago recommends the use of "quoted in" for the note:
  
  
  Ian Hacking, The Social Construction of What? (Cambridge, MA: Harvard University Press, 1999), 103, quoted in Manuel DeLanda, A New Philosophy of Society (New York: Continuum, 2006), 2.
  



That said, do not cite Wikipedia in a formal document (unless, perhaps, you are actually writing about Wikipedia or collaborative editing techniques). I love Wikipedia, and I believe it is reasonably well-maintained and has a lot of good information. However, you have no way to verify if the information in an article is true -- or, if you do have a source to verify it, you would just cite that source. Aside from the tired, "Anyone can edit it!" complaint, two severe issues with Wikipedia as a citation source are:


You get whatever version of an article stands at the exact moment your web browser fetches the page. No matter how hard Wikipedia's editors work, they can't stop a bad edit from reaching your web browser if it was made seconds before you fetched the page. Wikipedia doesn't undergo any kind of pre-publication review; all review is post-publication, which means you may see totally unreviewed information. (You can mitigate this by citing a specific past revision, but it still stands that a post-publication review process means that any given revision of an article could have claims that have been reviewed by absolutely no one except the author.)
In order for a reader or reviewer to ascertain the usefulness of a source, it must have an identifiable set of authors (or, for anonymous works, at least a consistent, reasonably small set of authors). Wikipedia makes that requirement incredibly difficult to satisfy. (Again, it's possible to satisfy this requirement if you cite a specific revision of a page and find out what contributors wrote each part of a page, but it is still difficult since a potentially huge number of contributors have helped build that revision.) It's hard for a Wikipedia article to be reputable where there are no clearly identifiable authors to which a reader could attach a reputation.