When your options vest, you will have the option to buy your company's stock at a particular price (the strike price).
Valuing the Options
A big part of the value of the option is the difference between the price that your company's stock is trading at, and the strike price of the option.
If the price of the company stock in the market is lower than the strike price of the option, they are almost worthless. I say 'almost' because there is still the possibility that the stock price could go up before the options expire.
If your company is big enough that their stock is not only listed on an exchange, but there is an active options market in your company's stock, you could get a feel for what they are worth by seeing what the market is willing to buy or sell similar exchange listed options.
Exercising the Options
Once the options have vested, you now have the right to purchase your company's stock at the specified strike price until the options expire. When you use that right, you are exercising the option. You don't have to do that until you think it is worthwhile buying company stock at that price.
If the company pays a dividend, it would probably be worth exercising the options sooner, (options don't receive a dividend). Ultimately you are buying your company's stock (albeit at a discount). You need to see if your company's stock is still a good investment.
If you think your company has growth prospects, you might want to hold onto the stock. If you think you'd be better off putting your money elsewhere in the market, sell the stock you acquired at a discount and use the money to invest in something else.
If there are any additional benefits to holding on to the stock for a period of time (e.g. selling part to fit within your capital gain allowance for that year) you should factor that into your investment decision, but it shouldn't force you to invest in, or remain invested in something you would otherwise view as too risky to invest in.
A reminder of that fact is that some employees of Enron invested their entire retirement plans into Enron stock, so when Enron went bankrupt, these employees not only lost their job but their savings for retirement as well...