First, having the Vocaloid program. And then doing the following...
- Finding a public VSQ.
- or Creating a VSQ yourself.
- A music file of the song you want to cover.
- and Depending on the situation, you may or may not need permission of the original creators for each media mentioned.
If you want to know how to work with the Vocaloid program, it is a trial-and-error situation that only you can do. If you want to know phonemes and such, please see Vocaloid wiki page Phoneme List. Making a decent cover song with a Vocaloid does require you to have more than just the Vocaloid program, you should look into various audio programs (such as FL Studios) to tweak the voicebank and song.
Internet Co. has an online shop of downloadable music data: http://shop.ssw.jp/dl_data/. Each data package is as cheap as 315 JPY and consists of three files: a VSQ file, an instrumental music file in WAV format, and MIDI file of the instrumental. The shop seems to be aimed at the domestic market of Japan; the web page is written in Japanese language, and almost all of the songs are Japanese pops and anime songs.