I have a lot of different apps on my iPhone, but I find that they are not arranged in a way that is useful to me. Is there some way to move them around or group them so I can find the ones I want to use most often?
It is very easy to re-arrange your applications on the iPhone.
If you select the application and hold your finger down, all the application icons will start to wiggle. You can then drag the icon from its current location to where you want it. You can drag it to the right or left edge to move it to other pages. When you're done, click the home button to get out of "wiggle" mode.
You can also create a folder containing groups of applications. Imagine you want to group all of your games in a folder. Hold down the first applications icon and when it wiggles, drag it on top of another game application and drop it on that application. This will create a folder with the two applications. (The phone will "guess" the appropriate name for the group. You can change the name at this point, if you like.) Now you can drag more icons into that folder. Click the Home button when you're done.
You can also use this same technique to delete an application. When the icons starts to wiggle, you will see an x in the upper-left corner of each user-installed application icon. Select the x to delete the application. You will receive a confirmation that you actually do want to delete the application. Be carefull because you may lose any data you have saved that's associated with this app, and may not be able to recover that data even if you re-install the application. Also remember to remove the application from iTunes so it doesn't install again.
If you sync your phone using your computer and iTunes, you can also arrange your application icons from within the iTunes application.
These steps work equally well on an iPad.
You can accomplish the same goal on Android phones, using the information found here.