How to restore app icons

If they are native apps that came with the phone - you may have hidden them by accident

Settings - General - Reset - Reset home screen layout

If these were apps you bought

You can re download them for free from the app store or

Connect to iTunes - sign in - click on My Purchases - then apps - click install

In addition to the suggestions that ManSinhamade, it is also possible to restrict certain apps which would make the apps disappear from the screen. Safari, FacetIme, iTunes the App Store and News can all be restricted which will hide the icons. Settings>General>Restrictions is where you can check aNed make sure they are not restricted.

Apps can also be placed in folders and you may have done so and forgot about it or did it accidentally. To find those apps, do a Spotlight Serach for them. Swipe down from the middle of any home screen to enable the search feature. Type the name of the app in the search field. When it appears in the search, the name of the folder in which it resides will appear to the right of the app name,

The native apps cannot be deleted, they are there somewhere. If the folders contained non-native apps and they were deleted, you will have to redownload them. To create new folders, press and hold an app like you are going to delete it but instead of clicking on the x move it into another app. A new folder will be created which you can name as you wish.

elcpu Has provided the information that you need for creating a new folder, but just to clarify, you will have to download the apps again which youncan do at no charge, as long as you use the same Apple ID that you purchased then with and you can find the apps in the purchased tab of the App Store app on your phone. Launch the App Store app and tap on Updates. Then tap Purchased at the top. Then tap Not on this iPhone and you will see all of your purchased apps that a re available for download.

Also - from within iTunes with the phone connected you can see which apps are not on the phone and click the install button

Not sure it is possible to delete folders with apps in them however

You might have hidden the apps using Restrictions.

Check your iPhone > Settings > General > Restrictions. If they are enabled, that's likely your issue.