Gear/approach to legimitately mining (not buying) a single Bitcoin
Bitcoins aren't mined individually; they're awarded to miners who discover a block.  This process is like a race that restarts every ten minutes when a new block is mined (the miner gets a block reward plus transaction fees).

In order to have a shot at winning these races, mining operations use expensive arrays of custom hardware.  So, without that, you would have a pretty slim chance of discovering a block before one of them did.