You didn't say what country you are in, and the answers will differ somewhat. These answers assume that you are a single American in your 20s with no dependents and a good job. You've probably done some of these already, but I list them just in case.
1) Establish a savings account, checking account, and no-annual-fee credit card. The interest rates on these don't actually matter that much, because you shouldn't keep that much money in the accounts, nor should you ever carry a balance on the credit card, so find accounts that give convenient low/no fee ATM access. Don't use your bank's investment services or advice; they usually suck.
2) Arrange to have your paycheck auto-deposited into your bank account.
3) Arrange to have all of your bills (utility, rent, insurance, etc) auto-debited from your bank account or (better) charged to your credit card. Have the credit card automatically paid in full from the bank account each month.
4) If your employer offers 401k/403b (retirement fund) matching, make sure you're taking full advantage of it.
5) Add up all of your expenses for a month, including loan payments. Accumulate 6x this amount in your bank accounts. This is your emergency fund. It also ensures that you don't need to worry about the day-to-day timing of paying bills, and should be enough to avoid any minimum balance fees on your accounts.
Got all that done? Good, you're already way ahead of most people. By routing your payments through your credit card, you start to build up a good credit rating. And with your bills automatically paid, you don't have to stress about accidentally missing a payment and screwing it up. Do review your bills every month to make sure the numbers seem correct. Make them send you paper copies of the bills if you need the reminder.
Now, on to stage 2:
6) Get some kind of financial software, and spend the time to learn how to use it. Download your bank statements into it every month.
7) Pay off all your debts (other than a mortgage), from highest interest rate to lowest rate.
8) Make a guess when you'll need to buy your next car, and how much it will cost. Start saving enough each month that you won't need a loan to buy it.
Okay, if you've finished all of the above, /now/ it's time to start investing.
9) Go to a discount broker like Schwab, Fidelity, or Vanguard. Open a Roth IRA. Set it up in your finance software. Divert as much money as you can to it, up to the legal limit (around $5-6k/year, unless you're making more than about $110k/year). Invest that money in index ETFs and mutual funds with no loads and low fees.
10) Still got money left? Go back to your employer's 401k/403b. Increase your contribution as much as you can, up to the maximum (around $17k/year).
11) Not out of cash yet? You must be in the software business. Okay, now we go back to your broker and open up a taxable investment account. Transfer your remaining excess money (after doing all the previous steps) into it. Now you should get a book on investing, and practice using this money.
Finally, remember the monthly expenses you calculated in step #5? Multiply that number by 500. That's your endgoal. When your savings reach that level, you can retire, and live off your investment returns forever. When you do, throw a party, and invite everyone from f.DS.
Good luck!