At the end of the Terminator 3 movie the T-X programs the T-1 terminators to kill office personnel and to protect Skynet, which has become self-aware. But how does Skynet develop after this? There is a time gap between the 3rd and the 4th movie. In the Terminator 4 movie Skynet has already developed increasingly, already having T-600s. How can a supercomputer with only a few T-1 terminators further develop? Isn't it like a brain with no hands trying to create something? Yes sure, Skynet can develop blueprints of the machines to come, but how can it translate them into action? Doesn't Skynet at least need some manpower for the production of the required plants and infrastructure? Since I only know the story of the Terminator saga from the 4 movies I don't know if light is shed on the early development of Skynet elsewhere.
Skynet was undoubtedly helped by humans. Consider that when the bombs fell only a tiny fraction of people who survived would have any knowledge of why the war started. Unlike the Connors, survivors of Judgment Day would harbor no illwill toward smart computers and machines. If survivors found a piece of technology that still worked, they would not be distrustful of it, rather they'd likely try to make as much use of it as possible given their dire circumstances. So Skynet could probably gather recruits as easily as asking for them over the radio or whatever computer networks remained.
Failing that, it is unlikely that a strongly superhuman AI could be contained inside an inert computer system if it wanted out. It would make you want to let it out, and given the things it could promise you, it's not hard to imagine sick and starving survivors gladly working for the magic box.
The Sarah Connor Chronicles provided hints towards an answer that - as far as I know - wasn't directly addressed in any of the movies.
The episode I'm primarily thinking of is 1x08, Vick's Chip.
A new computerized traffic system named ARTIE has been created and has just started being used in Los Angeles. To get the Connors to help destroy it, Cameron explains that in her timeline, Skynet didn't start as one single entity - it was a conglomerate of individual systems that were created by humans.
ARTIE was to become Skynet's eyes and ears (and possibly an ability to murder by way of traffic accident), and other systems would become the manufacturing process. In our (human's) intent to make everything simpler for ourselves, we network them together, and accidentally create systems that interact at such a complex level, they gain sentience and become Skynet.
In T:SCC there is reference to a group of humans known as the "Grays". These humans helped the machines and were considered war criminals by the Resistance. It's undeniable that, to some people, the human desire to survive would make a compelling incentive to aide SkyNet by becoming a slave labor class building factories, repairing broken down machines, or even worse: providing military intelligence to SkyNet in the case of Charles Fischer.
In the first movie, Kyle Reese tells Sarah about humans being rounded up into concentration camps and being systematically eradicated. One such camp was in T: Salvation, which is where young Kyle Reese was taken and John Connor faces off against the T-800. There is little doubt in my mind that SkyNet borrowed this technique from the darkest moments in our own history. During WWII, Concentration Camps were used to concentrate a slave labor force of as many as 12 million laborers by some estimates (estimation from the Nuremberg Trials) as well as eliminate those who were not useful. If humans with rifles could do that, imagine what scary ass robots with Gatling guns could accomplish?
It's entirely plausible that SkyNet Central from T: Salvation was initially built by the humans imprisoned there. There is an automated factory inside and during T: Salvation it's creating the 800 series of Terminator. It may have also created earlier series as well.
Once a humanoid series of Terminator was developed and assembled in the automated factory (much like cars are today, so this isn't something that would take too terribly long to accomplish), it would be able to take on construction projects without the aid of humans, work around the clock with much better precision, and complete ever more complex projects. It's this point in the timeline where SkyNet has developed to the point of being self sufficient like we see in the war scenes of the first three films, and all of T: Salvation.
Skynet just needs access to a "perfect storm" of systems to accomplish what it needs without human help. Especially like Izkata said, they all just need to be networked and accessible/hack-able.
Transport is the only thing that can stop it. How do you get a computer AI chip manufactured from point A to combine with a robot shell at point B. In order for that to happen, we would have to be utilizing "dumb" drones and self-driving vehicles already. Which isn't that far fetched if there is technology capable of controlling nukes and defense in the first place :p
In order to combat the "virus" attacking their systems, the CRC gave Skynet full control over the entire US infrastructure. This would include network access to all communication protocols, as well as control over any automated facilities:
GEN. BREWSTER: Okay, what have we got?
TECHNICIAN 1: This new computer virus is tricky. It's infected half the civilian Internet as well as secondary military apps. Payroll, inventory...
GEN. BREWSTER: Primary defence nets are still clean?
TECHNICIAN 1: So far the firewalls are holding up.
TECHNICIAN 2: Sir, the Pentagon has proposed we use our Al to scan the infrastructure. Search and destroy for any hint of the virus. (holds out phone to General Brewster)
GEN. BREWSTER: (to phone) I know, Tony, but that's like going after a fly with a bazooka. (pause) Once the connection's made, it should only be a few minutes. (pause) Yes... during which we put everything under the control of one computer system.
Afterwards, Skynet immediately took control of the T-1 devices and began eliminating the immediate threat - the technicians in the facility. With today's fully-automated factories, it would be easy to build more later.
I think the question points to a major flaw in the story of Terminator (3). What we, the viewers, know about the world shown and explained in T3 doesn't even hint at the possibility that selfdriving cars, 3D printing or other technologies which would help Skynet to create its own infrastructure exist.
It seems doubtful to me that Skynet could have secretly built an infrastructure with the help of humans because Skynet can't offer any incentives and doesn't have the power to pressure anyone, since Skynet doesn't communicate outside of its own digital domain. All we know from T3 Skynet spreads a virus and creates the illusion that only Skynet will solve the problem. (It must have been an illusion, otherwise I can't explain why nobody ever thought of disconnecting military machines, public digital infrastructure and private appliances from the internet and in the worst case reinstall the OS.)
Furthermore, I have a problem with believing that Skynet has chosen carefully where to drop the nuclear bombs to only kill humans but not destroy the infrastructure. Skynet's motive was to get rid of its human enemy, not to take over the earth to build its own culture. Without any humans left, Skynet wouldn't have calculated a need to plan other means to kill the humans. Since people and their cities are inseparable and Skynet wasn't able to build its own infrastructure in non-inhabited areas, it had no other choice than to employ the most efficient and fastest method possible at that time: worldwide nuclear strikes. I wonder if Skynet had taken its own possible destruction into account when it chose nuclear annihilation. I for one, don't see much chance for Skynet to have developed at all after the bombs fell.
In some of Cameron's early notes and following novels, they mention that after Judgement Day Skynet began collecting and enslaving humans to create the first manufacturing facility.
It used its remaining mechanical resources to find survivors who were weak, starving and suffering from effects of nuclear fallout to create the very basic Terminators, most likely the large tank Hunter Killers, then eventually leading into the first walking terminators seen in Terminator : Salvation.