There are many ways to find new apps, but you will need to focus your search:

     Things to Consider Before Using an App with Students:

     What is the intended use of the app?  Game? Skill and Drill? Project Creator? Research? Assessment?

                                                                                                                             (Formative vs. Summative)

     How does the app meet the targets for the lesson or unit?

     Is an internet connection required?

     Is an email or registration required?

     If a project creation app, how will the teacher view the final product? (Email option? VGA capabilities?)

     How long will the app be in use and can multiple students use an app simultaneously?

     Things to Consider Before Purchasing an App:

     Which Common Core Standards does this app support?     

     Cost?     (With Apple's Educator Volume Purchasing Agreement the district must pay for each individual app

                    purchased per device)

     How often do you plan to use the app?

     Ease of use for students?  / Grade level appropriate?

     Reviews from other users?  Have you tried the app yourself?

     Is it ad supported or have links to external sites?

     Is there sufficient time for library staff to download app to devices?

     Online Sites For App Searching:   

Apple -the App Store

Apple's main source for it's apps is the itunes store which can be downloaded from this site.  Or users can search from here with apps are divided into categories with popular ones listed first and then allows users to search alphabetically.  

i-tunes Store:

Use an ipad to search directly in the i-tunes store or download it from a desktop.  Search under education and check out the New and Noteworthy, Apps for Every Subject or Apps for Teachers.

Appshopper:

Search by category or type in a specific app name.  This app allows users to create a wishlist and will send an email when a wishlist app becomes free.  Search the Popular Recent Changes for i0S to see which apps are free that day.

Appymall:

Search by category or click on FREE APPS to see all the free apps for that day. Apps are listed with title, developer, grades and goals.

Digital Storytime:

App reviews with categories, prices, etc.

Smart Apps for Kids:

Sign-up for the free app alert and receive an email each day listing free apps.  Search by age and/or subject.

Theimums:

Apps are categorized by age or category and on Fridays they offer their FAST 5 which are their top five recommended free apps. Sign-up to receive as an email.

YouTube:

YouTube is a great resource for researching apps.  Search for educational apps to see what other teachers are using and how they are using the apps or search for tutorials/reviews about specific apps.

KinderTown:

The KinderTown app helps busy parents find the best educational apps for kids ages 3-6 years old. Download it on your iPhone, iPad, or iPod Touch and teach your little one something new today.

Common Sense Media -App Reviews

Get age appropriate reviews of apps by our expert editors.

Geeks with Juniors -App Reviews

Geeks With Juniors is a weblog about (geek) parenting and technology. Our posts are mostly iPad/iPhone app reviews showcasing the best apps on the App Store.

App Star Picks

AppStar Picks is a unique and innovative app that provides a smart way for you to discover a catalog of over 320 best apps for kids that have been thoroughly independently tested and reviewed just for you.

Teachers with Apps

Apps used and reviewed by teachers for teachers.

Fun Educational Apps

Best fun and educational apps for kids for iPad/iPad Mini / iPhone/ iPod Touch. Kids apps review for math, spelling, language arts, science, social studies, languages, early learning, storybooks, games ... And follow up daily deals and free app offers.

AppAbled

App advice for the special education community.

Apps by IEP Goals/Skills

From Technology in SPL Education website

Integrate iPads Into Bloom’s Digital Taxonomy With This ‘Padagogy Wheel’

http://www.edudemic.com/2013/05/integrate-ipads-into-blooms-digital-taxonomy-with-this-padagogy-wheel/