Quickest way to share an iOS app
Update (September 2019)

Some of the information provided in the answer is no longer valid (specifically discussed in point #1), due to the changes introduced in the subsequent releases of iPhone hardware and iOS 13 software. They are discussed in the latter part of the answer.

The original answer applies well to iPhone equipped with 3D Touch hardware capability, and running iOS 12 or earlier supported version of iOS. Here's a list of iPhone that shipped with 3D Touch hardware:


iPhone 6s/6s Plus
iPhone 7/7 Plus
iPhone 8/8 Plus
iPhone X
iPhone XS/XS Max




Original Answer

It is not possible to share an app directly from one iPhone (iOS device) to another. What can be done instead is to share the App Store link for the app. Your friend can then install the app from the App Store onto their iPhone. There are different ways you can share the App Store link with your friend. I'll list them down, starting with the simplest and quickest one.

1. Using 3D Touch Quick Actions:

iPhone 6s and newer (excluding iPhone XR), namly 6s Plus, 7, 7 Plus, 8, 8 Plus, X, XS, XS Max include a feature called 3D Touch. It gives users an additional mechanism to interact with the iPhone by using pressure to peek into and pop open content on iPhone. This is a hardware feature built into the display, and is not available on any other iOS device (iPod touch, iPad mini, iPad and iPad Pro).

You can use use Quick Actions to easily and quickly share the link for the app with your friend. On your iPhone, go to the Home Screen, locate the app, and apply a little pressure on the app icon until the iPhone gives a haptic feedback and reveals the Quick Actions menu like this:



Now simply tap on the Share Odyssey item to reveal the Share Sheet. You can AirDrop the link to the app to your friend, which will directly reveal the app in the App Store on your friend's iPhone. He/She can simply proceed to install it.



To use AirDrop, you'll need to ask your friend to enable it on their iPhone. AirDrop can be turned on by going to Settings app → General → AirDrop and tapping on Contacts Only or Everyone. AirDrop can also be turned on from the Control Centre (revealed by swiping from the bottom of the screen on the model of your and friends iPhone).

This is the quickest, easiest and the most newbie friendly way to share an app from one iPhone to another.

2. From your App Store purchase history:

Open the App Store app on your iPhone. Now tap on your profile picture shown at the top right. Tap Purchased to see the list of all the apps that you have bought and are linked with your Apple ID. Make sure All section is selected at the top.



Now locate the app in question from the list. You can also use the Search facility if your list of apps is lengthy. Once you have filtered down to locate the app, tap on the app icon to reveal the App Store page. Now tap on the blue circular button with three dots to reveal the action sheet. Tap on Share App... item to open the Share sheet. You can choose the usual sharing options to share the app with your friend (AirDrop, Messages etc.).



3. Searching on the App Store:

Quite often, the display name of an app (the one shown below the app icon) differs from the actual name. Searching the App Store by the display name shows the app in the results in most cases (you may have to scroll through in some cases). To search for the app, open the App Store app, tap on the Search item and enter the app display name in the search bar.



Once you have located the app under the search results, simply tap on the icon to reveal the App Store page for the app. Now tap on the blue circular button with three dots to reveal the action sheet. Tap on Share App... item to open the Share sheet. You can choose the usual sharing options to share the app with your friend (AirDrop, Messages etc.).

4. Searching on the Web and sharing the link:

You can also search by the app name or the display name on Web using a query similar to "app name + iTunes link" (Odyssey + iTunes link in this case). This is sometimes more efficient than searching on the App Store. (There's no right or wrong approach, the search logic for App Store and Web search work differently).

 

Now once you have the link for the app, you can share it by any suitable means as discussed above with your friend. When searching on Web on your iPhone, tapping on the link opens it directly in the App Store app.



The app in question is a beautifully designed game called Alto's Odyssey. You can share the following App Store link for the game with your friend:


https://itunes.apple.com/app/altos-odyssey/id1182456409




Update

3D Touch, a hardware feature has been subsequently been removed from the recent generation of iPhone. The functionality is simulated using a software based feature called Haptic Touch. Instead of detecting a physical pressure on screen, long tap is detected, and the device provides a Haptic feedback using the build in Taptic Engine in iPhone 6s and later (barring iPhone SE). Here's a screenshot from an iPhone 7 running iOS 13 with Haptic Touch in action for sharing App Store link to an installed 3rd party app.



Long press was earlier reserved to make the app icons wiggle, so that users can easily uninstall or rearrange apps, move them into folders and rename folders. As Haptic Touch has taken over it in iOS 13, the options are now made available in a similar menu as peak menu shown earlier. While earlier, an app could only display a share command, now every 3rd party apps shows at leat two commands, namely, Rearrange Apps and Share App.

Performing either a 3D Touch or a long tap on the devices that have the 3D Touch hardware, presents the same peek context menu.

iPhone XR, introduced in the year 2018 was the first iPhone to get rid of the 3D touch hardware, while the concurrently introduced iPhone XS and XS Max retained it. 2019 line of iPhone, namely, iPhone 11, iPhone 11 Pro and iPhone 11 Pro Max all got rid of the 3D Touch hardware. They all rely on Haptic Touch to offer the similar functionality as discussed in point #1 above.

One of the earlier iPhone models, namely iPhone SE lacked 3D Touch hardware but supports running iOS 13. Since Haptic Touch is a software based feature, it received the similar functionality, which was not available previously.





P.S.: A quick and informative guide on difference between Haptic Touch and 3D Touch can be found here:


Haptic Touch vs 3D Touch: What's the Difference?