On a good graphing calculator, use the STAT function and choose CALC. Assuming you've already entered a table of data, it gives you several options: linear regression, logarithmic regression, exponential, power (to several orders), trigonometric (fitting a sine curve to the data), etc. I'd have to look at the manual to remember the details of the process, but the result is an equation that will recreate the same pattern.
I usually use Excel, since it's on just about every computer and spreadsheets are almost always more functional than entering data into a calculator.
In Excel, once you've plotted your data, you can add a trend line. The options for the trend line are similar to the options on a graphing calculator, with the advantage that as you select each option, you can immediately see how well the trend line matches the plotted data. The disadvantage is that Excel doesn't offer a trigonometric option, a major drawback. You can come close using a higher order polynomial, but it's not as good. (On the other hand, if you've taken basic trigonometry, it's really fairly easy to fit a sine wave to your data, when appropriate, even without the aid of a computer or calculator.) When you have a trend line that comes close to matching your data, select the option to display the equation on the chart.
Just looking at the plotted data should give you a decent clue of the type of equation that would model it best, so you usually only have to try a couple of options regardless of whether you're using a calculator or Excel.