A Dispensationalist Perspective
This question needed some input from a dispensationalist point of view. That has been the attempt here.
First, let me state that I (generally) agree with what has been posted thus far that:
Theology affects hermeneutics, but is not itself a hermeneutic.
The hermeneutic circle entails that dispensationalism is both a
theological framework and a hermeneutical approach. One's theology
will affect the reading of the text and one's reading of the text will
affect one's theology.
Similarly, user1985's statement
Most all theological frameworks will affect how you read a text, and
thus bring hermeneutic principles with them. But the theology itself
is not the hermeneutic, although it may imply some.
There are aspects of the concept of the hermeneutical circle that I have issues with, but still, in general I agree with how theology can feedback and affect reading. Dispensationalism is not excluded in this, along with all other theological frameworks.
A Clarification of Dispensationalism Itself
Let's start by letting Charles Ryrie define the essential essence (sine qua non) of dispensationalism, since he is a recognized leading traditional dispensationalist (and the leading one regarding defining of it).1 He does have three points (which differ from some points others have noted):
"A dispensationalist keeps Israel and the church distinct" (46).
"This distinction between Israel and the church is born out of a system of hermeneutics that is usually called literal interpretation ... historical-grammatical hermeneutics" (47).
"The underlying purpose of God in the world ... [is] the glory of God" (48).
There are "variations" of articulation for #1 among dispensationalists, but the principle is generally valid as a distinguishing feature. This is not unlike that there are variations of articulation for covenant theologians regarding the covenants of works, redemption, and grace.
There are many dispensationalists that would put point #2 first,3 since point #1 derives from point #2 (even as Ryrie himself states; I'm unclear why Ryrie put them in that order, but probably because #1 is the key difference between dispensational theology and covenant theology's replacement theology).
Point #3 is really not a big issue for our discussion here about hermeneutics, but points #1 and #2 are. Mike Stallard made a needful clarification to Ryrie's point #2 (which Stallard puts as point #1), and phrased the three points like so (from page 34):4
- "The preservation of the literal interpretation of the Old Testament at all points of theologizing in the light of progressive revelation"
- "A distinction between Israel and the Church"
- "A doxological purpose of biblical history"
When he states, "at all points of theologizing in the light of progressive revelation," what he means is Old Testament priority over New Testament priority in forming theology. That is, the difference in dispensational and nondispensational hermeneutics is the starting place (OT or NT, respectively) of applying the literal hermeneutic (19); that the New Testament should not be "read back into the Old" (22). This is because God revealed Himself in a progressive way, so at each step of the revelation, there was a message (a meaning) He was conveying to the people then, one that does not get overridden (i.e. the Church replacing Israel) by His later revelation (else He "lied" in the previous revelation), only clarified by it.
Answering the Question Given Here
 Is dispensationalism a theological framework or a hermeneutical
approach?  If the latter (or if it is somehow both) what does it
prescribe in terms of how a given text should be understood?
Dispensationalism is a theological framework grounded in a literal (grammatical-historical) hermeneutical approach that gives priority to following the order of divine revelation in coming to an understanding of the text and theological conclusions.
I've already affirmed it is not the latter (i.e. a hermeneutical approach, though in a sense as already noted in the agreement above, it is "both" as one's theology or worldview framework always influences one's hermeneutics). Rather, it in fact holds to a literal hermeneutic. For an understanding of that, I suggest examining some of the basic/intermediate textbooks on the topic used in some dispensational schools (at undergraduate/graduate level).5
Some Final Clarifications
Dispensationalism is named for its understanding of there being "dispensations," which user1985 generally noted correctly that it refers to "how God deals with people in different time periods," and the OP himself essentially has a correct understanding of in the question. One of the things Mike Bull correctly states in his answer is that "the idea of 'dispensations' is not unbiblical," and you will find the term in covenant theology books as well (though not entirely with the same meaning and/or implications). This broader recognition is why Ryrie and other dispensationalists do not count it as a sine qua non, even though it is what "named" the view (45).
Such period divisions have been recognized throughout church history, as is another commonly associated teaching of dispensationalists, premillennialism (a form of chiliasm).6 Contra user1985's footnote, there is much more "history" behind the view than is characterized by those who only believe it goes back to John Nelson Darby. It is only true that (1) the maturity of the viewpoint came about at that point and since then (much like other points of theology were not recognized immediately after the penning of the NT scriptures), and (2) the Scofield Reference Bible popularized the view.
What is important to realize is that all these things (and more) that dispensationalists hold to is what we believe arises from the proper application of a literal (grammatical-historical) hermeneutic. And far from being anachronistic (as user1985 claimed in his footnote), by having OT priority in interpretation, the dispensationalist seeks to understand the OT as the Israelite would have, something many Christians abandoned early in church history. Christ's coming revealed more, and clarified much, but it did not override God's promises to His people Israel.
1 The following three quoted points are from Charles C. Ryrie, Dispensationalism, Chicago, IL: Moody Publishers, 2007. This is a revision of his 1995 work of the same name, which in turn was revised from his first work on this titled Dispensationalism Today (1966). As you can see, he has been writing about the topic for over forty years.
2 Note: I'm using "traditional dispensationalist" to distinguish from the more recent divergence of what has come to be known as "progressive dispensationalism," which in part attempts to argue there is no sine qua non as Ryrie puts forth. The distinction is not without relevance, but for purposes here is simply to give you an awareness of this internal debate among self-proclaimed dispensationalists. While I would recommend anyone interested in learning more about dispensationalism to start with Ryrie's book before wading into the controversy, for those interested in a comparative study of the two branches, see Herbert W. Batemman IV, ed., Three Central Issues in Contemporary Dispensationalism: A Comparison of Traditional and Progressive Views, Grand Rapids, MI: Kregel Publications, 1999. For initial statements on progressive dispensationalism itself by advocates of it, see Craig A. Blaising and Darrel L. Bock, ed., Dispensationalism, Israel, and the Church, Grand Rapids, MI: Zondervan Publishing House, 1992; and Craig A. Blaising and Darrel L. Bock, Progressive Dispensationalism, Grand Rapids, MI: Baker Books, 1993.
3 For a revised order, see Mike Stallard, "Literal Interpretation, Theological Method, and the Essence of Dispensationalism," Journal of Ministry and Theology 1 (Spring 1997), 5-36. This article would be well worth reading if one wanted to get a better grasp of traditional dispensationalism.
5 Roy B. Zuck, Basic Bible Interpretation: A Practical Guide to Discovering Biblical Truth, Colorado Springs, CO: David C. Cook, 1991; Henry A. Virkler and Karelynne Gerber Ayayo, Hermeneutics: Principles and Processes of Biblical Interpretation, 2nd ed., Grand Rapids, MI: Baker Academic, 2007; Walter C. Kaiser, Jr., Toward an Exegetical Theology: Biblical Exegesis for Preaching & Teaching, Grand Rapids, MI: Baker Academic, 1981; E. D. Hirsch, Jr., Validity in Interpretation, New Haven: Yale University Press, 1967. Also, a popular dispensational book that gives one viewpoint of a dispensational eschatology includes hermeneutical discussion in its first four chapters, J. Dwight Pentecost, Things to Come: A Study in Biblical Eschatology, Grand Rapids, MI: Zondervan, 1958.
6 For a thorough survey of church history regarding divisions of history, see Arnold D. Ehlert's nine part series "A Bibliography of Dispensationalism" in Bibliotheca Sacra issues 101-103 (1944-1946). Also see, Larry V. Crutchfield's article, "The Early Church Fathers and the Foundations of Dispensationalism," Conservative Theological Journal 2 (March 1998), 19-31. There are also people considered Covenant Premillennialists, which is why premillennialism is not a sine qua non.