For the classic Sanger sequencing you need quite large amounts of DNA to be able to run the sequence reaction. This is a problem when you want to sequence whole genome since the DNA needs to be amplified then, which for some sequences can cause problems, introduce errors or cause bias.
Single molecule sequencing is a huge step forward here, since only one molecule of DNA is used for sequencing. There are different sequencing technologies based on this principle.
The system of pacific biosciences uses a polymerase bound to a small well which binds a singlestranded DNA and begins to make the opposite strand, when nucleotides are present.
See the image below or this video, which explains the technique quite nicely.
Illumina binds singlestranded DNA molecules to the surface of the reaction chamber and starts amplifying them there. The use of fluorescently labelled nucleotide allows to monitor the reaction. This looks like the following (left side of the figure from the review mentioned below):
An illustration from Illumina which is more detailed, can be found here.
Although it is a bit older (and the technology develops fast), this review is a nice introduction: "Sequencing technologies - the next generation."