How do I find a recently deleted app from my iPhone's Home Screen?

If you just removed the app from your Home Screen and did not choose the Delete App option, then it is in your App Library. Swipe all the way to the left to get to the App Library, then swipe down on the screen to view the apps alphabetically. There is no way to sort them by recently removed from the Home Screen, but you should be able to identify the app you are looking for.

If you go to the App Store, click your profile icon in the top right corner, click "Apps", and then click "My Apps", you should be able to view all apps you've downloaded that have been saved to the Cloud, including ones not currently on your device. If you carefully scroll through, you may recognize an app that you should have downloaded. You can also wait until you find yourself looking for the particular missing app and realize it's the one that's missing, then proceed to redownload it.

To re-download a deleted app, you would have to go to the App Store and download it again. If you don't know the name of the app you deleted, I'm not sure there is anything else you can do to find it.