A very simple implementation would be to plug you computers speaker jack into you hi-fi - load iTunes (or one of many others) to play the music or stream internet radio - voila!
If it's a more recent computer, it may have an optical output or USB, so you could progress to the next level.
Next level would be to include a DAC - affordable/quality units like the schiit bifrost at $350 - see review - will give you pretty good quality sound
http://www.tonepublications.com/review/the-schiit-bifrost-dac/
And from there the world is YOUR oyster
Then you can get into the hi-def stuff - but ensure the DAC you choose supports the sample rate you want to get to.
Also, some dacs support different maximum sample rates for optical vs s/pdif vs USB - just be sure to check before you buy
And yes - cable quality does matter - I like DH Labs - great quality at reasonable price.
You have to decide what you want - simple, or better sound, or even for ultimate portability - Bluetooth from your cell phone
Your choice