"The subject of our inquiry is substance; for the principles and the causes we are seeking are those of substances." (Metaphysics, I, 1.)
In his Metaphysics, Aristotle uses 'substance' as a technical term rather than a general one, with a specific set of meanings and definitions. In very broad terms, 'substance' is all of those things which "are not predicated of a subject but everything else is predicated of them" (Metaphysics V, 8). This makes it a useful starting point for any inquiry into the nature of things.
In general, when we speak of substance, we are speaking of "the simple bodies, i.e. earth and fire and water and everything of the sort, and [...] bodies composed of them, both animals and divine beings, and the parts of these" (V, 8). Thus substance can be thought of as analogous to matter -- it is simply the basic stuff out of which everything is made, "if the universe is of the nature of a whole" (XII, 2).
The reason that corporeal substance is a good starting point is that it is the first kind of being, in three different senses. First, it is "the ultimate substratum, which is no longer predicated of anything else" -- that is, it is that which is at the bottom of everything, with nothing below it, in terms of things being predicated upon other things (V, 8). The second sense of substance is "that which, being a 'this', is also separable" -- i.e., as it is that of which all things are predicated, it can be divided such that other things may be predicated of it. Consequently, the substance also underlies "the shape or form of each thing" (V, 8). The third sense in which corporeal substance is the first kind of being is the simplest, and it is purely chronological: if the universe is indeed a whole (which for the purposes of this discussion is taken as a given), "it coheres merely by virtue of serial succession", so "substance is first, and is succeeded by quality, and then by quantity" (XII, 1). That is, the matter underlying the form must necessarily precede it; for it is not possible to modify (in number or in features) that which does not yet exist.
With that aside, we can address the properties of substance (i.e. its principles). Aristotle says that there are three, and they arise from the last sense of substance as described above; "two being the pair of contraries of which one is definition and form and the other is privation, and the third being the matter" (XII, 2). The matter is the base substance that persists indefinitely -- undergoing changes in quality, quantity, place, etc., but remaining at its core fundamentally unchanged: for matter is matter (or substance is substance) regardless of its characteristics. Definition and form are the characteristics that the matter takes on when it is subject to causes (about which more presently); and privation is a sort of negative characteristic, a not-having of some attribute.
Aristotle's description of privation is deliberately very broad, because limiting it would prove an impossible task; for in fact there are "as many kinds of privations as there are of words with negative prefixes [or, more broadly speaking, contraries]" (V, 22). For instance, a man can have sight or be sightless; a thing can be visible or invisible. But privation does not only refer to this kind of black-and-white duality, where some characteristic is either possessed or not possessed by a given thing -- it can also refer to a partial having of that characteristic. (Aristotle's example is that only a man who is sightless in both eyes is called 'blind'; a one-eyed man is not called 'blind' despite his being blind in one eye, a partial privation of sight.) There are shades of grey in privation, and "[t]his is why not every man is 'good' or 'bad', 'just' or 'unjust', but there is also an intermediate state" (II, 22).
That there is such an intermediate state is definitive proof of the enduring nature of substance -- that which somehow persists beyond change. It is helpful for clarifying this point because of the example that it provides: if something changes in its attributes, for instance a leaf's changing colour from green into red, the contrary colours do not themselves change -- they are only attributes, and thus "there must be something underlying which changes into the contrary state" (XII, 2). Furthermore, the contraries do not themselves persist; obviously enough, once a leaf has changed from green to red, it is no longer green. And so there has to be some third thing that passes between the contraries as something undergoes change -- that is, the matter, or the substance.
Aristotle's celebrated four causes -- formal cause, material cause, efficient cause, and final cause -- are what initiate change in substance and guide its form and definition. Formal cause is "the definition of the essence, and the classes which include this (e.g. the ratio 2:1 and number in general are causes of the octave), and the parts included in the definition" (V, 2) -- in other words, formal cause is the shape that something takes. Material cause is that which is most closely akin to matter; it is "that from which, as immanent material, a thing comes into being" (V, 2). (For instance, the material cause of a bronze sculpture is the bronze from which it was sculpted.) Efficient cause is "that from which the change or the resting from change first begins" -- like an artisan is the efficient cause of a bronze statue; and lastly, final cause is "that for the sake of which a thing is [or an action is performed -- for final cause is not limited to just things]" (V, 2). For example, the final cause of an acorn is an oak tree -- it exists for the sake of actualising an immanent purpose of becoming a fully-grown tree.
In substance, which is the unity of matter and form, the causes and principles overlap. This is because the causes themselves tend to coincide: in fact, formal, efficient, and final cause can be grouped together (form), while leaving apart material cause (matter). We begin by bringing together the formal and final causes: for formal cause, the shape that a given thing takes, is the same as final cause, that for the sake of which it exists. An example is that of an oak tree: its immanent formal cause is the shape that it takes (i.e., the tree), and its final cause is the same (i.e., actualising itself as a tree). These two can be thought of as the same in all cases in the natural world; for everything natural seems to exist in the shape that it does (formal cause) for a reason (final cause). Thus formal cause and final cause are the same.
Efficient cause can also be grouped together with formal and final cause under the broader principle of "form" (or "definition"). This is particularly true in the case of things in nature -- which contain within themselves a principle of motion -- but it can also be said of artifice. Broadly speaking, efficient cause is that which makes something into something else, or what causes a change (in anything, not just in itself). For instance, in the Physics, Aristotle gives the example of a father's being the cause of his children; and so too it is with all things in nature, with like begetting like.
Precisely because like begets like, the efficient cause of something is identical with the form that it produces by its efforts. Returning to and building upon the example of an acorn and an oak tree: the formal cause of the acorn is that of the oak tree which it is becoming, as befits its species. Its final cause is also to grow into an oak tree (because formal and final cause coincide); and its efficient cause is the oak tree that begat the acorn, according to the idea that like begets like. Thus can all three of these causes be united into one principle -- form -- leaving only matter to be dealt with.
Material cause, as stated above, is more or less synonymous with matter. It cannot be brought together with formal, efficient, and final cause because it is that in which all of them are immanent (and of course it cannot be said to be immanent in itself; it already is itself). A second reason that it does not coincide with the other three causes is that it is that basic stuff upon which all of them act: efficient cause sets it in motion, formal cause dictates its shape, and final cause provides it with an inherent goal toward which it strives. So material cause is the same as matter; and the other three causes are the same as form, or definition.
The (corporeal) substance discussed previously is not the only type of substance for Aristotle; he also makes provisions for a different kind, one that is "eternal and unmovable and separate from sensible things", that is "without parts and indivisible" and "impassive and unalterable" (XII, 7). This substance is the ultimate cause; that "which moves while itself unmoved" and on which therefore all the functions of heaven and the earth depend (XII, 7). It is Aristotle's god, and without it neither causes nor principles could have any effect on corporeal substance whatsoever. In this way, substance is doubly the first kind of being -- not only chronologically or as the ultimate substratum as detailed above, but also as the ultimate source for all of the movement that defines nature as such.
Metaphysics is available online here: http://classics.mit.edu/Aristotle/metaphysics.html
and Physics is here: http://classics.mit.edu/Aristotle/physics.html
Unfortunately, neither of them have line numbers, so instead in the above I cited things slightly less specifically by book and section number. Them's the breaks.