A practical approach to starting saving is to Pay Yourself First - before you pay your bills, before you buy food, before you do anything else, set aside a portion of your income to save. The first bill you pay each month should be to yourself. This habit, developed early, can help a person to build up their wealth.
David Bach’s 2003 best-seller, The Automatic Millionaire, is devoted exclusively to the subject, providing a step-by-step guide to developing the saving habit and making it automatic. Bach calls his model the "tortoise approach" to becoming wealthy by retirement age.
There are a number of sources on how to implement this - for example: here and here.
Here's a fun savings analysis tool to play with, if you haven't got the message yet.
One way to start (in the UK, at least) is with a 'Regular Saver' Account that pays (often unbeatable) high rates of interest on regular lump-sum payments for up to a year. After that time you can transfer the capital to an easy-access high-interest account (Level 2 of the Income Pyramid).
Finding the best current Regular Saver account can be a bit of a challenge - but the DIY approach is to look at something like Moneyfacts or Moneysupermarket
For example, in January 2011 HSBC bank was offering a fixed 10% rate of interest for up to £250 invested each month for 12 months (but you will need an HSBC current account).
No faster way to start your Money Snowball rolling...
I am not a financial advisor and the information provided does not constitute financial advice. You should always do your own research on top of what you learn here to ensure that it's right for your specific circumstances.