In my opinion, the best way to save money is to automate your finances as much as possible and include a "pay yourself first" savings feature.
Automation helps remove the decision-making process which is often influenced by our emotions, timing or other factors. If you set it up to take a specific dollar amount or percentage from each paycheck and deposit it into a savings account, investment account or retirement account, and build the rest of your cash flow planning and bill paying around the net-of-savings amount, you'll be saving and building your wealth without having to think about it and make a "should I or shouldn't I" decision every pay period.
For some great tips on how to setup financial automation and include a savings component, I suggest you check out the thorough guest post by Ramit Sethi on the blog of Tim Ferriss:
Be DEDICATED to saving. Set up an account where money is automatically deducted from your paycheck or bank account at regular intervals. You will become used to not having this additional money to spend and eventually your next egg will grow.
All the advisers have great ideas. I think the key to saving money is to start. Start by working hard at your job and making a nice living, always trying to better yourself along the way. Secondly, by controlling your expenses and being a little cheap when you want something you don't really need. For instance, Starbucks coffee is expensive so go to McDonalds or drink at work instead. Those little lifestyle changes add up quickly in your savings. Also stop charging on your credit card, if you have no cash then you don't buy!! Have a goal to save say $200 a month and keep it in a separate account and don't touch. Having an emergency fund with 3-6 months expenses should be priority one to your saving plan. Good luck and start saving today, you will be surprised by how much you have one day!
Alexsandr - First an foremost, focus on saving money via instruments that are tax-advantaged. Your number one focus should be in funding the maximum allowed in your company 401k. This money is not only saved pre-tax, it is often matched by your employer, at least up to a certain amount.
The math is very compelling; If you contribute $1.00 to your 401k and your employer matches it, you have $2.00 to invest and all the growth is tax-deferred until you withdraw. If your full tax bite is, for example, 30%, what would you rather have on your $1 of gross income, $.70 or $2? We have all seen MANY examples of people who take the $.70 instead of the $2.00 because they are tight on cash. What a mistake! If you have a pre-tax savings vehicle at your job, fund it to the fullest of your ability.
Agree with both Russ and Julian. One more point; some like the idea of having multiple accounts for different goals; i.e.. House account, Retirement, Education, Trip around the world.. etc.. You can have a Brick and Mortar Bank account for checking and savings as the core.. then set up multiple on- line accounts ( I use Schwab Bank) and have as many accounts as you want and not worry about fees or minimums. They even let you "Name" each account which you see on your summary screen.. House .. Retirement etc.. this way you know which monies are for each objective and you can then invest appropriately. This is particularly useful approach for a freelancer or self employed. Good luck