There are basically 3 approaches:
* Full DNA sequencing. This is a multi-million dollar effort taken on by large collaborations, usually to generate a reference genome sequence for a species or particular line. Typically a variety of methods are used, from 'shotgun' style illumina, 454 longer reads, and now some newer even-longer-read methods. Long reads are important for generating accurate assemblies. Generally, some tricky portions will need to be meticulously amplified and sequenced with traditional Sanger sequencing to clean up. This gives you a complete sequence, including all inter-gene sequences, repetitive portions, etc.
* RNA sequencing. This method is the core of many molecular biology labs; you take expressed sequence (i.e. RNA that has been transcribed from DNA), reverse transcribe it to DNA, and then sequence the DNA. This gives you sequence information about the expressed part of genes (this is limited, though, because during the assembly process you'll reject many reads that don't map onto the reference sequence in standard analysis) but mostly gives you an idea of the relative expression of different genes. When people talk about gene expression going up or down in certain mutants, conditions, etc., they're usually talking about RNAseq (or qPCR if only a few loci are involved).
* 'Sampling' in this case refers to chips with various DNA fragments on it. You pass the sample DNA over it, and compatible sequences hybridize together, which is then detected via florescence. These chips are designed to carry sequence fragments that vary in the population. Together, these variants form a DNA profile. The quality of this profile depends on the design of the chip. The sequences included are generally loci that are known to affect particular diseases or to be especially variable in the population for assessing ancestry.
In cost magnitude, this goes from millions to thousands to tens.