Check through your carrier
Checking your data usage through your carrier is perhaps the easiest and most precise way to go. The four major U.S. carriers each offer an iOS app for their subscribers, and each of those apps lets you see your data usage for your current pay period. You can find apps for AT&T, Verizon, Sprint, and T-Mobile in the App Store.
The built-in way
If you'd rather not download and install another app, you can use some built-in tools to track your usage. Open the Settings app, then tap Cellular; here you'll be able to view how much data you've used in the current period, how much data each app has used, and how much talk time you've used.
But there is one catch: You'll need to manually reset the stats each month to get a more accurate picture of your data use. Otherwise, your iPhone will keep track of your data usage from the point you first activated it. To reset the stats, scroll to the bottom of the Cellular settings screen, then tap Reset Statistics. Confirm that you want to reset the stats, and iOS will zero out your stats.
You'll want to reset this screen once per month, to correspond to your cell plan billing cycle. To remind yourself, you'll want to add a recurring event to your calendar.
Open the Calendar app, then tap the "+" button. Go ahead and give the calendar entry a title--something like "Reset data usage stats" works--and set the event to repeat each month on the first day of your billing cycle. You'll want to set an alarm, too, so you get a notification when it's time to reset your usage stats. Once you're set, tap Add. Now you'll be all set to keep on track and avoid going over your data cap.