I had an employee ask me what the process was to buy stock options, so I figured I'd answer this question publicly so anyone interested could understand & benefit from it.

The way company stock options work is as follows:

As an employee, a company will grant you a pool of options.  Let's say you get 10,000 options.   Those options typically won't "vest" all at once, meaning that although the company has promised you those options, you receive them on a specific schedule known as a vesting schedule.  That schedule is usually something like the following:  "4 years, with a 1 year cliff".  What that means is that they vest over 4 years (so 25% of the options become available to you each year) on a monthly basis for as long as you're an employee.  So if you're an employee for the next 27 months after the option grant, then you'd vest 27/48ths of the total, or 56.25% of your total options (and 10,000 x .5625 = 5,625 options vested).  The "cliff" means that in the first year, you don't vest monthly, but rather annually.  So in the first year, if you only stay for 11 months, then you don't vest any of the options.  But if you stay for 12 months, then boom-- you vest 12/48ths (or 25%) of the options granted.  The reason companies do this is so that if an employee doesn't work out in the first year, they don't have an obligation to grant any options.  (It would be awkward to hire an employee for 3 months who it turns out isn't a good fit for the company, then have to fire that employee, but still have to vest 3/48ths of his or her options).

OK so you have these vested options.  Now what?  

Granted options have a "strike price" -- the price at which you can pay to turn them into stock.  Let's say that the strike price is 50 cents each.  That means that if you stayed at the company for 27 months after the grant, and you vested 5,625 of your options, it would cost you $2,812.50 ($0.50 x 5,625) to purchase your options and turn them into stock.