If you're like most people, by the time you get around to paying all of your bills and covering expenses, there's not much left of your paycheck for savings. "Pay yourself first" is a helpful expression to remind you that your savings should be thought of as an expense, just like food or housing, and should be included in your budget.
Make saving part of each paycheck a priority: See if you can have a set dollar amount directly deposited to your savings account by your employer (which many do, and is an easy way to begin saving). If you don't see the money, you won't be tempted to spend it. Think of it as paying yourself before paying anyone else.
No matter how well you prepare your budget, you will run into unexpected expenses. Whether it is a relatively minor cost like a parking ticket, or a more serious one such as car repairs, you'll eventually be forced to pay for something you hadn't planned on.

It's a good idea to set aside three to six months' worth of living expenses in an emergency fund for these unexpected expenses. Using the example of $50,000 in expenses, this means between $12,500 and $25,000 in such a fund. Although it may seem like you can't afford to save that much, experts would counter that you can't afford not to save. Remember, you don't have to create the full emergency fund all at once. You can budget for it too.
Once you've established an emergency fund and prepared for all the expected expenses in your budget, you can really start saving money. If it feels like you're just scraping by and can't afford to save, here are a few tips for finding that extra dollar or two:

Reinvest any money you make on existing investments like mutual funds or stocks, as opposed to having any dividends or gains sent to you via separate check
Deposit a big chunk of cash gifts or bonuses from work before they disappear — consider this "found money" and save it
Bringing lunch to work one day each week could save you $20 or more each month
If possible, write yourself a check at the end of each month when you pay your other bills, forcing you to save
Washing your car by hand may save you $10 or more each month
Take advantage of any matched-savings programs that may be available to you, such as employer matches on some 401(k) savings plans
Eliminating one fast-food meal and eating at home each week could save you $15 each month