1. Introduction
iPads and other iOS devices rely on the use of an iTunes account to download and manage apps.  Using the same iTunes account on multiple devices allows you to purchase an app once and use it on all iOS devices you own.  Android's Play Store accounts work the same way -- however please be aware that you cannot access Android apps on an iOS (Apple) device, and vice-versa; the same app may exist in both stores but will have to be purchased separately.
The school's iPad management system requires students to create an AppleID with their school-issued email address to receive the apps and books that the school has purchased.  These 
accounts are created without using a credit card, so through these accounts the students can only access free apps.  This account must remain logged in to the App Store most of the time for this transfer to happen periodically throughout the year, but students and parents can log out the account temporarily and log in with a personal account to access paid (and free) apps that they have purchased with personal gift cards or credit cards.  We don't recommend applying gift cards or credit cards to school-issued email accounts, as these accounts do expire after graduation.

2. iTunes, iCloud, So Many Places to Sign In
When you look at Settings on your iOS device, there are lots of places where you can log in and out of accounts: iTunes & App Store; iCloud; Mail.  These accounts do not all have to be the same.  iTunes & App Store is your app, book and music purchases.  iCloud is your online storage and backup.  Mail is your linked email addresses.  You can sign in/out of these accounts as needed; however parents will need to know their students' passwords if they want to log out and back in, otherwise they will need to alert the student that they are no longer signed in.
A word of caution - do not sign out of iCloud unless absolutely necessary.  iCloud is your automatic backups, as well as your connection to Find My iPad.  Logging out of iCloud shuts these off, and puts your data and device safety at risk.  You do not need to sign out of iCloud to change accounts in iTunes/App Store.

3. Changing iTunes Account Sign-In
To switch iTunes accounts so that you can access apps purchased on a different device, first tap Settings.  On the left-hand menu, select iTunes & App Store.  Tap on the signed-in user name (email address), then tap Sign Out.  It may take a few seconds for the sign out process to complete.  Next, tap Sign In.  Then input the Apple ID (email address) and password that you want to obtain apps from.  It will take around 10 seconds for the changes to finish.  Then you can go to the App Store app and either select new apps to purchase/download, or tap Purchased at the bottom of the screen to see apps already owned by this account.  Once the apps have finished installing, you can go back to Settings and Sign Out, then Sign In again with the school-issued email address.  When you need to update those apps in the future, you will need to sign in as the Apple ID that downloaded them.