"As much as you can" is the standard advice. Many financial planners recommend that you save 10% to 15% of your income for retirement, starting in your 20s.
But that's just a general guideline. This is your retirement we're talking about, so it pays to get a little more specific by doing your homework up front. It's a good idea to establish a savings target - one that tells you roughly how much you should set aside over time to meet your retirement goals.
The best way to determine your savings target is to use an online calculator like this one. It will help you figure out how much you should accumulate and how much you must set aside in the meantime to reach that target. Be sure to update the calculation each year, so that you can see if you're on track.
As a general rule, you'll need at least $15 to $20 in savings to cover each dollar of the annual shortfall between your income and your expenses. So for example if your projected retirement expenses exceed Social Security and pensions by $20,000 a year, you might need a nest egg of $300,000 to $400,000 to bridge the gap.