These are standard instructions on using iTunes to updates the apps on your iPhone/iPod.
Alternatively, you can click App Store on the iPhone/iPod and tap Updates in the bottom navigation menu to see a list of updates. However, updates are frequently not shown here due to a bug in the App Store, hence the instructions below to use iTunes to update your apps if needed:
1. Launch iTunes 2. Connect your iPhone/iPod to your computer. 3. Sync your iPhone/iPod to iTunes. 4. In iTunes, select Applications in the list on the left under LIBRARY. Sometimes a number is shown next to Applications in the list indicating the number of applications you have that need updates. 5. Click Check for Updates at the bottom of the screen in iTunes (or iTunes may already tell you that you have updates such as "4 Updates Available"). 6. Click on "4 Updates Available" - for example. 7. You will see a screen listing all updates that are available. 8. You can click to update only one app. Or you can click Download All Free Updates near the top right hand portion of the screen in iTunes. 9. After they have been downloaded ( you can track their progress by clicking Downloads in the list on the left under STORE in iTunes), sync your iPhone/iPod again to iTunes. 10. Many times you may need to power down and turn your iPhone/iPod back on. Hold the power button down for 5 seconds until you see the "Slide to power off" message. Slide to power down your iPhone/iPod. Wait a few seconds and tap the power button again to turn your iPhone/iPod back on.
The update process for apps on the iPhone does have quite a few bugs in it. Here are some links that discuss those issues if you are also having a hard time:
Here is a link from Apple that is helpful as well: http://support.apple.com/kb/TS1702