Simplest way to understand it is to first figure out your tax brackets for Federal, State and Local. It's a progressive rate, meaning that the first $30k you earn is taxed at one percent, the next $50k is taxed at a slightly higher amount, the next $60k is taxes an even higher rate, and so on. If you find the rates, it should tell you the exact thresholds.

Then figure out what your taxable income is. It should show this pretty clearly on the W2.

If you main or lost any money gambling or in the stock market, you can include that too. However, if you earned money on a stock that you held for at least a year, those earnings are taxed at a lower rate than regular income for federal.

If you have dependents, then figure out how much you can deduct or credit from them.

I assume you are probably going to use the "standard deduction", which you can also look up with the tax brackets. Subtract that from your new taxable income.

With your final taxable income minus deductions, you can the use the different federal, state, and local tax brackets to check how much you are supposed to owe. Compare those values to what was withheld on your W2.

If you notice a discrepancy, you can take a look at any of your paystubs. Multiply your gross pay by an amount for it to represent your annual pay. So if you get paid biweekly, multiply by 26. Do the same for each the Federal, State and Local taxes on that pay stub. Compare those taxes withheld against the values you calculated before. They should be pretty similar. If they aren't, then it's because your employer didn't have an accurate value for your dependents or couldn't predict your total annual income when they issued each paycheck.