I agree with @drio that there is no single tool. So your best bet is to

1. master a scripting language (or many). Learn the bioinformatics libraries available for that language.

2. learn linux command-line tools (grep, awk, cut, and others).

3. learn the most used bioinformatics tools. e.g.:

   • one (or preferably many) short-read aligners

   • samtools

   • an NGS viewer (IGV is a good one to start)

   • Bedtools

   • A means to view and filter your NGS reads

   • and certainly many others depending on your specific focus.

4. Then start to learn some of the common data repositories. e.g.:

   • UCSC and MySQL server

   • Ensembl

   • 1000 genomes

I haven't seen it listed yet but bioconductor has a massive collection of different tools for high-throughput analysis. There is also galaxy, which is quite nice. It wraps a lot of the tools already mentioned in other answers.

There is no one stop tool.

What people does is to rely in a few set of tools (PICARD, samtools, GATK, bwa) and build their own pipelines and scripts on top of that. You add other core tools depending what type of next-gen projects you are working on( re-sequencing, RNA-seq, de-novo assembly, etc ...)

BTW, I wrote a package manager that I use to quickly deploy my toolbox in new machines. If you look at the recipes directory you'll find the names of those tools.

here is a long list: http://seqanswers.com/wiki/Software/list

A scripting language will get your job done. However, using tools off the shelf will save heaps of time in the long run. A lot of tool packages exists with all the tools you need for basic sequence analysis. None of these tool packages interact very well - which is a shame. It would be interesting, if they shared a common interface. The one in Biopieces is very simple and straightforward. Here are a few tool packages I remember on top of my head:

1. Samtools
2. Bedtools
3. FastX toolkit
4. EMBOSS
5. Biopieces