Starting a savings plan can be very difficult, especially if you're already limited financially.
Remember that it's okay to start small. If you continue to put off the thought of savings because you only have an extra $5 here and there, you'll probably never get it started. Do a little research at your bank. Find a savings account that offers interest but doesn't have a minimum balance requirement. I personally started by opening an account for my newborn child, because child's accounts were the only ones that didn't require a minimum balance and they earn interest on any balance, even if it's as small as one dollar.
The next step is to find ways to contribute to the account. Save your pocket change and at the end of the month deposit it into that savings account. Return bottles and cans. Deposit any money you have left over from last week on the morning of your pay day. Money you earn on the Internet, either through Helium or other various money making sites you may belong to can also go into this account. Even if it is only a few dollars here and there, remember a little in abundance is a lot.
When balancing your check book, especially if you use your debit card a lot, round every transaction up to the nearest whole dollar amount. Let's say you spend $1.35, in your check book note it as $2.00. You now have an extra 65 cents to put into savings. At the end of the month add it all up and deposit that into the savings account. It will add up to a lot of money very quickly.
After you've accumulated enough money you can transfer it into an account that pays more interest so you are adding even more to it.
The most difficult part of savings comes once you have a bit of money in an account. It can be exciting to see your balance and you may think of different ways you can spend that money. This is why many people, especially those with limited income, have trouble saving. Train yourself to only use your savings in true emergencies. Fight the urge to check the balance frequently. Put the money in there, then forget about it. Keep in mind while the money stays in the account it is constantly earning you even more money. Remind yourself why you wanted to start saving in the first place and remember you can't get there if you spend it now.