The theory of saving for emergencies such as job loss, illness etc and putting away 10% of your monthly income for such events, is a good one. But, what do you do is that 10% is the difference of ...
It isn't possible to save money while you have debt. If you really want to save money...pay off your debts.
For example, if you are putting money in the bank and the interest earned is 3%, and you have a credit card that is charging you 10%...you aren't using your money to your advantage.
Starting with your smallest debt, begin taking any extra money you have and pay it down every week or month until it's paid off. Then go to your next smaller debt and do the same. Every time you eliminate one bill, you have that amount of money to pay toward the next, so it begins to snowball. Once you've paid them all...you've just given yourself a monthly raise. At that point, take the raise (you've given yourself) and add 10% out of your income and start saving.
For emergency purposes, a good rule of thumb is to have 6 months of expenses set aside for emergencies. Once you've saved that amount, go to the next step, which is investing for the future.
When investing, think tax deferment. Start funding a ROTH IRA every month and consider mutual funds (less risky than stocks with a decent rate of return).
Saving is a lot easier than it sounds but it takes discipline. You can do it.