Manually editing and converting among these file formats is easy enough to do, but it's also time consuming and may introduce human error. Instead, I like to use tools or scripts that automate the process. Here are my top choices:
1) ALTER (ALignment Transformation EnviRonment)
This online tool can convert alignment files to and from the following formats: NEXUS (.nex), Fasta (.fa or .fasta), Phylip (.phy or .phylip), ALN, GDE, MEGA, MSF, PIR. It can be found at this address: http://sing.ei.uvigo.es/ALTER/
Simply upload your alignment file, select your output format, and convert. The converted file will download automatically to your computer.
ALTER is incredibly easy to use, completely free, and does not require a software download. My only complaint is that the site goes down pretty frequently, so it's good to have one of these other options up your sleeve:
PGDSpider is a powerful java-based tool for file conversion that can be run either from command line or a GUI. "PGD" stands for Population Genetics Data, so many of the file formats are common to population genetics data (microsats, SNPs, etc.) and software (Arlequin, Structure, etc.).
PGDSpider is intuitive enough to use. It's not quite as simple as ALTER, but it's also much more powerful in terms of the number of file formats it can handle. It can parse 31 and write to 34 different file formats.
The PGDSpider website notes that it is not capable of handling large NGS datasets, which may make this final option more appealing:
3) Custom scripts
I'll be honest: I'm no good at writing code. However, I'm a ninja when it comes to finding other people's code online and tweaking it when necessary. A simple google search reveals many, many existing scripts for file format conversion in several different languages. A search for "Perl convert fasta nexus" brought me to this script, and "python convert nexus phylip" took me here. This is the path I usually take for file conversion with large datasets.
There are a lot of other options out there (e.g. this online tool) but those listed above are the ones that I am most familiar with. What's your favorite?