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Launch iTunes on your computer and connect your iPhone to an available USB 2.0 port via an Apple dock connector cable.
Click "Apps" in the Library section of the sidebar in iTunes. This displays all of your purchased apps.
Related Reading: How to Authorize a Computer to Put Apps on an iPhone
Click the "Updates Available" link if one appears. If no such link appears, none of your iPhone apps need to be updated.
Click "Download All Free Updates" if you want to update all of your apps at the same time. If you are already signed in, the updates will start downloading to your computer. If you are not signed in, enter your Apple ID and password and click "Get." Wait for all updates to finish downloading before moving on to the next step.
Click the "Get Update" link adjacent to any individual app you want to update. Wait for the update to finish downloading before moving on to the next step.
Click the name of your iPhone in the left sidebar, then click "Sync" to transfer the updated apps to your iPhone.