If you are new to building an emergency fund and you are wondering how much you should start with, 
it is important to start with small, short-term goals. If possible, start with a goal of $500, then work your way to saving half a year’s worth of living expenses. Having an emergency fund can help you avoid getting into financial binds such as taking out our using a credit card or loans. See below for tips on how to build an emergency fund:
Create goals: Start with setting an overall financial goal for how much you would like to save. Then, create a monthly savings goal for how much money you would like to put aside each month to help you work toward your large savings goal.
Move money into savings account automatically: If direct deposit is an option with your employer, you may want to consider automatically dividing your check in half with a percentage deposited to your savings account and a percentage deposited into your checking.
Save your change: If you pay in cash when making purchases or for financial transactions, if you ever have change left over, take it back home and put the remaining change in a jar. Once the jar is full, you can deposit what’s in the jar into a savings account. There are also savings apps on your smart phone that you can use to process any remaining change from transactions into a savings account such as provide examples and link.
Save your tax refund: Your tax refund is another way to put some extra cash aside during the year. If you are expecting a refund, it’s a good opportunity to have it redirected to your savings account. Another option is to adjust your W-4 so that you can have less amount of money withheld from your paychecks each month and instead redirect it into your savings account.
Information derived from nerdwallet.com