After you receive your data from the sequencer, you will normally use a tool such as bwa to align your sequences to a reference genome. Most users will have a reference genome for their species. You can read more on reference genomes in the next chapter.
The most common representation for aligned data is the Sequence Alignment/Map (SAM) format. Due to the massive size of most of these files, you will probably work with its compressed version (BAM). The compressed format is indexable for extremely fast random access (for example, to speedily find alignments to a certain part of a chromosome). Note that you will need to have an index for your BAM file normally created by the tabix utility of samtools. Samtools is probably the most widely used tool to manipulate SAM/BAM files.