Form W-4 provides information to your employer's payroll department that helps them deduct the right amount of withholdings for any taxes you may owe at the end of the year. The employer takes taxes out of your paycheck each pay period, according to how you fill out the form, and then when you file your income taxes you essentially reconcile the withheld amount against the amount you actually owe, and either pay the difference or receive a refund. Essentially, the W-4 is an estimating tool.
You will need to fill out a W-4 for any job where you're being paid. Since you're describing that you have two jobs, you will need to fill out one for each job. The W-4s for both jobs must be filled out to account for your overall situation - if you start a second job part way through the year and it significantly changes your tax standing, you should file a new W-4 with the first employer to adjust the taxes they're withholding. Similarly, when you fill out the new W-4 for your new second job, you need to account for income from your first job. Otherwise, you may discover that too little tax has been withheld when you file your tax return next year.
The IRS provides instructions on the form:
They also provide an online calculator which you can use to help you decide how to fill the forms out:
Using this calculator, you can determine how to fill in the W-4 for your new job, as well as any adjustments you may want to make to the W-4 you filed with your first job. The calculator is a great tool that gives you specific instructions about what to put in what boxes once you've given it some basic data on your jobs. If you have a recent paystub handy from your first job, that will be helpful in knowing how to fill in the calculator form correctly.