Denaturing gradient gel electrophoresis is a method that established the "melting point" of the DNA (usually PCR fragments). When DNA denatures, especially when provided with a high melting temperature "clamp" in one of the primers, the stokes radius, increases (dramatically if clamped) and the migration slows such that the band of DNA stays in place. Thus DNA fragments can be characterized by how far they migrate. It is often used for sequences that are conserved such that PCR primers will amplify the DNA from many closely related organisms, e.g., the gene for 16S RNA. DGGE can then provide some information about the what organism contributed tot he band. It remains an approximate method.
If I am reading you question correctly-conventional agarose gel allows you to visualize the DNA of a certain size, but if it is a mix of DNAs you would not be able to notice it or separate different individual species DNAs. In DGGE you basically use an urea gradient that allows separating the DNA bands of the same size (since your PCR product is obtained by using only 1 primer set), but of different GC content. Therefor, you can just visually see any changes between different samples containing mixed DNAs, and, more , you can excise those individual bands, clone them and get their phylogenetic affiliation. DGGE is advantages if you are using DNA from complex environments/populations and monitoring changes in these populations, so you can save time and energy in sequencing or cloning them all.
That is actually not that hard. Short description is this. First of all you have to dye your gel and scan it under the scanner to see where the bands are located. Then you cut the bands from the gel, and from each individual band extract the DNA by a kit. then you have to make sure you cut the right band, so you should repeat the DGGE with your mixed DNA and individual band DNA. if it is what you want, now you have DNA to clone/sequence.
There are plenty tutorial sonline, as well as youtube videos. Good luck