Get in the habit of putting away 10 to 20 percent of your take home pay (after taxes, benefits, and maxing out your company 401k match) per month. Have it deposited into a dedicated bank account or automatically transferred at each pay date. Make it so that you never even see the money and learn to live on the rest of your pay check.
As you get your annual increases or promotions, make sure you also increase you savings amount (i gradually increased from about 10% right out of school to about 25% of a much higher take home amount in my 30's). If you can get into the habit of living below your means you'd be amazed how easy it will become to put away a pretty significant amount of money per year, especially once you reach the higher income levels of your 30's. Keep in mind that you won't be depriving yourself of too much as youll still be allowing yourself to increase your spending over the years so don't worry about all of the 'you can't take it with you' naysayers.
You'd be amazed at the peace of mind and confidence that having at least 6 months of living expenses in the bank and a large chunk of relatively disposable cash on hand can provide. If you've ever wondered how relatively normal people can pay cash for a fairly expensive car - it all starts here.