OP, my experience tells me there are really 3 main types of benefits that are related to company stock and I will start with your question - Stock Options:
1. Stock Options. When given options, the company gives you a set number of shares that you are given the choice (option) to buy at some point in the future. In most companies, these "vest" over a certain numbers of years (3 or 4 is my experience). This is a "waiting period" where you do not have actual access to do anything with all or a portion of the stock. An example will likely help:
Today, your company gives you 300 shares at a strike (option) price of $20. They vest over three years, meaning 1 year from now, you are able to exercise the option to buy 100 of them. A year after that, the next 100 becomes available, and then next year, the final 100 become available. In almost all cases, you have a TOTAL WINDOW of 10 years to make a choice to exercise.
Let's say in Year 5, price is now $50 per share. You can exercise your "option" to buy all 300 (or any part of the 300) for $20 per share. Most people do not exercise their option and then hold the stock - they exercise and sell immediately, in a cashless transaction as described by a prior poster above. In this case, if you exercise all 300 options, you would have a gross amount of $15,000 and subtract the option purchase price of $6,000 (300 shares X $20 option price) for a net of $9,000. This would, in today's tax world, be taxed at long term capital gains rates - likely 15%. If you only exercised a portion of your options, the math changes but the concept does not.
2. Restricted Stock Units (RSU's). These are "better" stock incentives in my opinion because they are stock that is simply given to you on a vesting schedule (you do not have to "buy" them). Same example as above - you are given 300 RSU's today with a strike price of $20, with 100 each vesting the next 3 years.
At the end of year 1, you are given 100 shares of the company stock at whatever price it is at on that day - let's say $30. Important to note here that the ENTIRE amount (100 shares X $30 per share) is considered taxable as income in the year in which the RSU is granted. If you hold onto it, you have a further tax event later on once you sell where you would be subject to either short term or long term capital gains based on the difference in price between the $30 and whatever you sell it at.
3. Employee Stock Purchase Plans. These are what geekette mentions above - money is taken our of your paycheck over the course of a period (usually 6 months) and then on a specific date, stock is purchased and you are given a discount from the price on that date (usually 15%). Some plans (including the one I participate in) allows the company to give you a discount on the stock price at EITHER the beginning of the purchase period or the end. Example below:
Beginning period stock price = $20
Ending period stock price = $30
Employee paycheck deduction = $100 over 13 pay periods ($1300)
At the end of the period, the employee has $1300 that will be used to purchase stock. The stock will be purchased at a 15% discount of the beginning price, since it is lower. So the purchase price is $17 per share (15% discount from beginning price) that the employee gets 76.47 shares ($1300/$17 per share). The employee can immediately sell for the gain - 76.47 X current price of $30, or $2294.10. This would trigger a taxable event at the individual's tax rate of $994.10 (2294.10 sales price minus the $1300 initial investment). If the individual holds the stock for at least a year, it would get preferential tax treatment of long term capital gains rates. The risk there is you do not know what the stock price will do in the next year.....
OK, hopefully that is helpful. What you are describing in OP are #1, but thought I would provide some addition info on the other things that have been mentioned here as well.
TC