Prima autem et manifestior via est, quae sumitur ex parte motus. But the first and more manifest way is, that which begins from motion.
1. Certum est enim, et sensu constat, aliqua moveri in hoc mundo. For it is true, and the senses establish, that some things are moved in this world.
2. Omne autem quod movetur, ab alio movetur. But every thing that is moved, is moved by another.
3. Nihil enim movetur, nisi secundum quod est in potentia ad illud ad quod movetur, movet autem aliquid secundum quod est actu. For nothing is moved, save according as it is potential to that to which it is moved; but it moves something according as it is actual.
4. Movere enim nihil aliud est quam educere aliquid de potentia in actum, de potentia autem non potest aliquid reduci in actum, nisi per aliquod ens in actu, sicut calidum in actu, ut ignis, facit lignum, quod est calidum in potentia, esse actu calidum, et per hoc movet et alterat ipsum. For moving is nothing other than drawing forth something from potency into act, for something cannot be reduced from potency into act, save through some actual being; thus actual heat (as fire) makes wood (which is potential fire) to be actually hot, and thereby moves and alters it.
5. Non autem est possibile ut idem sit simul in actu et potentia secundum idem, sed solum secundum diversa, quod enim est calidum in actu, non potest simul esse calidum in potentia, sed est simul frigidum in potentia. For it is not possible for the same thing to be at once actual and potential inasmuch as it is the same, but only inasmuch as it is diverse, for what is actually hot cannot at the same time be potentially hot, but is at the same time potentially cold.
6. Impossibile est ergo quod, secundum idem et eodem modo, aliquid sit movens et motum, vel quod moveat seipsum. It is therefore impossible that, in one and the same way, something could be moving and moved, or that something move itself.
7. Omne ergo quod movetur, oportet ab alio moveri. Therefore every thing that moves, must be moved from another.
8. Si ergo id a quo movetur, moveatur, oportet et ipsum ab alio moveri et illud ab alio. If therefore that by which it is moved, be moved, it must be moved by another, and that from yet another.
9. Hic autem non est procedere in infinitum, quia sic non esset aliquod primum movens; et per consequens nec aliquod aliud movens, quia moventia secunda non movent nisi per hoc quod sunt mota a primo movente, sicut baculus non movet nisi per hoc quod est motus a manu. But this is not to proceed infinitely, because then there would not be some first mover; and consequently neither some other mover, because second movers do not move save through being moved by a first mover, just as the stick does not move save through being moved by the hand.
10. Ergo necesse est devenire ad aliquod primum movens, quod a nullo movetur, et hoc omnes intelligunt Deum. Therefore it is necessary to come through some first mover, that is moved by nothing, and this all understand to be God.
You can find an alternative translation at New Advent.
Aquinas's argument has, I think, the following general structure:
A. Some things are moved. (this is #1)
B. Every thing moved is moved by another. (this is #2=#7)
C. Either there is a first mover or nothing is moved by another. (this is #9)
D. There is a first mover. (from A, B, & C; this is #10)
Then, as an interpretive comment on the argument as a whole: This all understand to be God, i.e., this fits the requirement of an argument for the existence of God, because something that is a first mover is something that has been considered to be God.
This is set up as a disjunctive argument; it could also, of course, be set up as a reductio ad absurdum (since the negation of the conclusion, combined with C and B, would conflict with A). It is valid.
While there are views that would question A (Humean views of causality, for instance, don't allow for an act/potency distinction, which is essential to the Aristotelian notion of 'motion'), clearly the premises that most need support are B and C. Sentences 2-7 are devoted to supporting B. Nor do I think it makes much sense to deny B; that would be like saying that something can change from potential to actual without there being anything actual that makes the change possible--in other words, giving up B in its Aristotelian sense is a fairly serious price to pay for rejecting the argument. Note that Aquinas considers the issue of infinite regress (#8 & #9) only as part of a subargument for the truth of C. In these he argues that, given the nature of the dependence involved in B, assumption of infinite regress would result in contradiction. It is worth pointing this out, because the importance of the infinite regress to the argument is sometimes exaggerated. It does play an essential role, since it supports the key premise; but the First Way itself is not structured as an infinite regress argument.
C is usually found by readers of the argument to be a bit puzzling--hard to interpret, and not very developed here. The reason for it is stated briefly as "second movers do not move save through being moved by a first mover", with the additional argument (in scholasticism, I find, examples are generally used as arguments, not as clarifications: an example is to induction as an enthymeme is to deduction) of the stick in the hand. It's common to accuse Aquinas of begging the question here, but I don't think he is--he's just being more concise than modern readers can usually follow.
In discussing (in SCG 1.13) Aristotle's reasons for rejecting the infinite regress, Aquinas gives the following as the third of those reasons:
** Id quod movet instrumentaliter, non potest movere nisi sit aliquid quod principaliter moveat. Sed si in infinitum procedatur in moventibus et motis, omnia erunt quasi instrumentaliter moventia, quia ponentur sicut moventia mota, nihil autem erit sicut principale movens. Ergo nihil movebitur. What moves instrumentally, cannot move unless there be something that principally moves. But if one were to proceed infinitely in moving and moved, all would be like instrumental movers, because they would be posited as moved movers, and nothing would be a principal mover. Therefore nothing would be moved.
And in the Compendium Theologiae (1.3), he says something similar. The point: to be a moved mover is to be an instrumental cause; but if there is no first cause, everything is an instrumental cause and nothing is an instrumental cause.
Consider the causal chain:
A <- B <- C <- D <- E..., where A is moved by B, and B by C, and C by D, and so on. In such a chain B mediates between C and A, and so is an instrumental cause for C; C mediates between D and B, and so is an instrumental cause for D. But, because we are dealing with moved, movers, one can say the same of cause-complexes: {B, C} is an instrumental cause mediating between D and A, for instance; {B, C, D} is an instrumental cause mediating between E and A. So we have two options: 1. We can trace it back to some principal cause; and then everything between the principal mover and A will be a mover moved by the principal mover. 2. We can trace it back infinitely; and then everything that moves A must be an instrumental mover, but what moves A will not be an instrumental mover, because it will not be moved by anything. In other words, on the infinite regress, we have a mover (what moves A) that is both moved and unmoved; and, as well, given that to be a moved mover requires that it be moved by something, the nonexistence of that thing means that it is both a mover and not a mover. This contradiction, I think, is the problem Aquinas sees with infinite regress. A similar result can be obtained by thinking in terms of intermediate rather than instrumental movers. Removal of a first cause from the series, then, seems to introduce a contradiction in which things would have to be both moved and not moved by a mover that is both moved and not moved, and therefore a mover and not a mover. The whole First Way could in principle be reconstructed in terms of actuality and potentiality, since motion is a particular case analyzed in terms of those concepts, although it would be complicated to do so. In other words, the Argument from Motion is not an argument from 'motion' in our sense of the term, but an argument from motus, in the scholastic sense. Motion is analyzed by Aristotle in terms of actuality and potentiality. It's the act of the potential insofar as it is potential. Because of this, Aquinas reads 'motion' as an imperfect actuality--it's the actuality of something insofar as it is potential to being something actual (other than it already is). Because act or actuality is a more fundamental principle than motion (as one of the things in terms of which motion is defined), acts are not motions (although beginnings of acts are). The act is to motion as the final result to the process geared to producing that result; it is the limit of motion, not itself a motion. Thoughts in themselves, being acts, are not motions (although beginning to think this or that is a motion). Thus for God to be self-thinking thought by nature would not indicate motion but pure actuality. Aquinas holds that the Platonists would call both motion and actuality 'motion', and allows that in this large, improper Platonistic sense of 'motion' God is self-moving mover. But in the stricter, proper Aristotelian sense, He is not, because is purus actus, pure act unmixed with any potentiality. It is this that is meant by "unmoved first mover". The argument is about actuality.
Note that what this means is that the First Way does not require that the world have a beginning. Aquinas agrees that the eternity of the world is a possibility. He thinks it is false, for reasons of faith, but thinks demonstrations on the subject are not possible. See the (for the Summa) long discussion at ST 1.46.1. But this is a different issue; the question of whether the world (or matter or motion) began is a temporal issue. Aquinas's concern in the First Way, however, is causal, and it is a causal question that is not dependent on whether the world began or not. This is especially clear in the longer discussion in the Summa Contra Gentiles (1.13), where Aquinas explicitly recognizes that Aristotle held the eternity of the world, and that "Catholics suppose this to be false". But "to this it must be said that the most efficacious way to prove that God exists is on the supposition of the eternity of the world," because if the universe began it would already be more obvious that God exists, but if the proof shows God to exist even supposing that the world never began to be, it is that much more forceful. So Aquinas would deny that the proof presupposes either position (the world began or the world has always existed); but would also insist that on the latter supposition you can see just how strong the proof really is. All that is really in play in the First Way is the actuality and potentiality of things.