I'd first turn it off, remove the battery, hold the power switch for a few seconds, replace the battery, then turn it on. If any hardware got hung, that will reset it. (It's called power-cycling - the hardware starts fresh.)
If that didn't work I'd try to clear the cache. If it still didn't work, it's time for a trip to a repair shop or your carrier.
Is there any way YOU can fix it? If it's a bad digitizer (the "touchscreen" part), I'd recommend against it, even though the Youtube videos make it seem simple. It's not until you've done a few, and you start practicing on dead phones, because you're going to destroy a few screens learning. It's cheaper in the long run to pay a shop to replace it. (If they won't without doing a factory reset - a lot of shops won't work on a phone without resetting it first - try a factory reset before giving it to them to see if that alone fixes it.)