Like Pierre suggested, there's not really a direct answer to your question. Let me see if I can clarify some things for you.

Initially, I thought you were asking about Genome Browsers that let you pull out existing parts of reference genomes. A reference genome is a consensus sequence intended for investigators to compare their own in-house sequences. A good example is the UCSC Genome Browser. If you're using bioinformatics software tools like the ones based on the Genome Analysis Toolkit, you would use these reference data in tandem with your in-house data.

If you use modern sequencing instruments, such as an Illumina HiSeq or MiSeq, you're going to get, after heavy software processing, a fastq file. This fastq file gives the calculated genomic sequence, along with a quality score for each base. You can then compare these genomic data to a reference sequence using a variety of tools.

I'm more on the systems engineerings/support side of bioinformatics, but I cut my teeth on real-world data analysis by following the Galaxy screencasts available here: Galaxy is simply a web-based front-end for many common bioinformatics tools. It came to mind, because it has plenty of options for pulling in data from a variety of genome browsers. If nothing else, it's a good link archive for finding various browsers. You can save the data locally once you pull it in. Check out the "Get Data" link at the top of the left-hand sidebar.

If you go to the link I gave you, you can use the screencasts and anonymously use the public Galaxy server to follow the screencast and analyse real data. Galaxy is also pretty cool because if you use the Visualization tools, you can see how your data mapped to a reference genome. All that is covered in the screencasts. Even if you don't end up using Galaxy, it's still a very nice introduction to NextGen sequencing data analysis in general.

What you seem to be asking about is the process of genome annotation which can (but may not) be completely independent from a genome browser. We normally think of a genome browser as a visualization (and analysis) tool for exploring a reference genome which has been sequenced, assembled and annotated already. There are many many layers of annotation for a genome. You are asking about one of the first and most important annotation layers. I.e., the prediction/annotation of genes in the genome sequence. Browsers allow you to explore the genome and these gene annotations as well as many other features of the sequence (regulatory regions, conservation with other species, etc). Having said that, the people who create and maintain genome browsers sometimes also play a big role in genome annotation. For example, when a new reference genome is added to the Ensembl Genome browser they will run their pipeline for gene prediction on that genome. See their documentation and references for a starting point.