Most of the work in mind uploading, like that in nanotechnology, must currently be in the realm of theoretical applied science, because we do not yet have the means to physically produce the relevant devices. To make progress, then, we must attempt to show that uploading could in theory be accomplished by this or that process. Though we cannot test these proposals by carrying them out, we can (and must) put them to trial against the current body of knowledge in physics, chemistry, biology, and neuroscience. Where gaps in our knowledge force assumptions to be made (which is especially likely with regard to neuroscience), these assumptions should be made explicit so that the weakness of the theory is known.
Electron microscopy (EM) offers adequate resolution, though the samples must be both small and very thin. Work is underway to increase these bounds, using high-voltage EM to increase sample penetration, tomography or optical sectioning to make effective use of greater thickness, and mosaics to increase the imaged area. These developments are well justified.
Magnetic resonance imaging (MRI, also called Nuclear Magnetic Resonance) can achieve roughly 1 mm resolution in an intact human brain -- a valuable achievement for neuroscience and medicine, but orders of magnitude lower than the resolution that uploading requires. The resolution of MRI is determined mostly by the steepness of a magnetic field gradient which is generated in the sample; when extended across the breadth of the head, sufficiently steep gradients appear impossible. However, much steeper gradients can be achieved over short distances; researchers routinely obtain 0.05 mm resolution in live rats. It may be that a properly built scanner could achive the desired resolution in brain slices which would be thin compared to normal MRI fare, but still large compared to EM slices. For example, the ability to image 1 mm slices with 10 nm resolution would surpass EM by several orders of magnitude. If this thickness could be increased to several millimeters, and the area extended to 0.01 m^2, then processing the brain tissue would become relatively straightforward.
Other techniques have various drawbacks. Light microscopy is limited by the wavelength of light to a resolution which is probably insufficient for uploading. Acoustic imaging suffers worse resolution still.
A related problem occurs with establishing 3-D structure from 2-D information. Several approaches currently exist (e.g., EM tomography), but researchers still trace structures of interest by hand, so that the computer can align the data for the reconstruction. This could be automated though a combination of image recognition and signal processing algorithms. Such automation is vital if a significant amount of neural tissue is to be scanned in a reasonable amount of time.
As to whether an upload will be implemented as a neural network, the answer is "no" if you mean the type that's typically studied today. These are too simplistic to easily replicate real neural circuits. However, there is a growing number of neuroscientists working with more realistic biological neural models (see, for example, the Computational Neuroscience Class Library). These will probably lead (eventually) to functional duplication of brain circuitry.
Research in neural networks continues to advance at an ever-increasing rate, and all such studies help answer important questions in neuroscience and simulation. Of particular importance to mind uploading, however, are the more biologically detailed simulations. An area ripe for research is the complete simulation of small nervous circuits or systems. For example, the nematode C. elegans has on the order of 100 neurons in its nervous system, all of which have been identified and characterized. The medicinal leech has about two orders of magnitude more, but there is a great deal of repetition among its body segments. Detailed physiological and modeling studies of such simple nervous systems will be invaluable in determining which physical characteristics are functionally relevant. It seems extremely likely that the first creature uploaded will be one of these invertibrates.