There are really only two ways that you can increase your savings. First, you can increase your income. Second, you can spend less. Some would say that there is a third option of investing, but this is really part of increasing your income.
Savings is important for many reasons. It involves planning for the future. It is delaying gratification. It means having more reserves for emergency expenses. It means a higher likelihood of retirement. It also gives you more freedom and flexibility in terms of your job and your lifestyle. And, of course, there is the magic of compounding interest.
In terms of trying to save more, you really need to look at both areas. You should see if there are reasonable ways to increase your income, without necessarily altering your life too much. You should also see where you can cut back on spending, again, with the preference of not having a significant impact on your lifestyle. However, in some cases, maybe you do need to alter your lifestyle.
Each individual and family situation will be different. If someone is earning $200,000 per year at a job and is barely saving any money at all, then the person should probably be looking at his spending habits first. Even if the person lives in an expensive place like New York City, there is still a major problem if you can't accumulate significant savings with such a high income. Perhaps the person could earn even more than the $200,000 per year, but my bet is that if he has trouble saving money earning $200,000 per year, then he will also have trouble saving money making $250,000 per year.
On the other hand, think about a person who is making $12 per hour and is saving almost nothing. He is probably not living a lavish lifestyle on such a low income, even if he is young and single. He will have trouble saving money with this income because you still have to pay bills such as rent and food. The most obvious thing for this person to look at is his income. He has to look at ways to earn more, whether it means getting a different job, working a second job, or starting a side business. It is important that if this person does find another job making a lot more money, that he not start spending all of this new found money.
In terms of increasing income with investments, this can be important once you have built up some savings. If a guy has a savings account of just $1,000, I don't think he has to worry much about his savings account earning him less than 1% interest per year. He has to concentrate on saving more money. Once he builds up a significant amount (say, $10,000 or more), then he should start paying a little more attention to where it is going.
If someone has a net worth of $500,000, yet only makes $40,000 per year, he really should concentrate on his investments. A good return on his investments could net him almost as much as his yearly income. In today's environment, I think someone with this much money should consider investment residential real estate, assuming it is in a decent area. Having $500,000 sitting in a money market fund does not make much sense.
One last important point is that you shouldn't forget to invest in yourself. If you need the right equipment to make a side business work, then you should consider the investment. If you need a certification to help in your career, consider it. If attending a seminar will help you in your endeavours, then maybe it is worth it. You shouldn't take on debt to do these things, but a $1,000 investment in education today that may net you thousands of dollars in the future should not be neglected. You will not get that same return in the stock market.