Step #1. Open a savings account, preferably one at a different bank than where your checking account is, and with a high interest rate. This way your money is working for you as you are learning to save. This is always a plus. I have found that if the money is a bit harder to get, then you're not as likely to touch it.
Step #2. Every payday deposit 10% of your take-home money into that savings account. More if you have it or less if you need to at first. The point is to start saving and grow from there. It doesn't matter if you can only save 1% at first, at least you are starting to save and hopefully you will try for 2% next month and continue to grow from there. Many times, it's easier to do this with a direct deposit. If the money comes out each payday before you even see it then it's not as likely to be missed. Make sure that you do not touch this money. This money needs to be saved for your future, or in case you lose your job, or for a major crisis. Let’s hope that a major crisis never happens, but just in case, you need to be prepared. I like to have around one years' worth of income in this account.
Remember not to get worried about having it all at one time. The idea is to start saving and work toward the goal. Don’t get stressed if it takes a while, even a long while, to get there. You will get there if you keep putting the money away. Just keep thinking of how good it will feel to have the nest egg in case you hit a hard time in the job market.
Now this same idea can be done another way. I actually started mine in an envelope (more on envelope style savings later) and put it in my safe. This style of saving only works if you have the willpower not to touch the money. You know yourself better than anyone, so you decide what works best for you.