If you could make saving as easy as spending, then you could easily establish a good habit of saving. You can ask your bank if they can link your saving and checking accounts via your ATM card. If you have a different account for different goals, you can add to each one a little at a time and before you know it, you have that saved amount you need for those unexpected bills.
When you get your paycheck, let’s say you are paid monthly, put what you need to live for that month into your checking account. If you put in more than that amount, you will probably spend it.
This system will limit you in your spending since you are not leaving yourself any extra to spend.
Then you put a little into each of your different goal account and what is left should go into an investments account. Any holiday bonuses you get at work, birthday money or cash from the garage sale should go here also. If your bank cannot link your accounts, then try talking to your employer about direct deposits. In this way you can have part of your paycheck put right into a savings account automatically and then it is done before you even see your money each payday.