1) Are you upgrading from an older iPhone?
Yes. Go to step 2
No. Go to step 8
2) Make sure you back up your old iPhone first
If you're upgrading from an older iPhone, you can transfer all its apps, data, and settings to your iPhone 5s or 5c. But to do so, you'll need to make a backup (via iTunes or via iCloud) of your information.
3) How to back up an iPhone using iTunes
It's worth checking that you are running the latest version of iTunes before you start. Select iTunes from the menu, and Check for Updates. To make a backup, or update an existing one using iTunes, connect your old device to the computer you normally sync it with via USB, open iTunes, select the device, and press the Sync button.
4) How to back up an iPhone using iCloud
If you are running iOS 6 or iOS 7 chances are you will already be backing up on a daily basis via iCloud. Check that it has recently backed up: your device will automatically make an iCloud backup once a day as long as it's locked, plugged in, and connected to a Wi-Fi network, and as long as you have sufficient space available in your iCloud account. It it's not updated recently you can manually force a backup by opening Settings and navigating to iCloud > Storage & Backup, making sure iCloud Back up is on, and selecting Back Up Now. Backing up via iCloud may take longer than via iTunes, especially if it's the first time, so if you are in a hurry it may not be the best option.
5) How to set up your new iPhone
Turn on your new iPhone 5s or iPhone 5c by pressing the oblong on/off button at the top right of the device. Once the device is on, swipe where it says 'Slide to Set Up'. Apple will now take you through a number of options including language and country, connecting to WiFi, Enabling Location Services, and then the option to Restore from iCloud Backup, Restore from iTunes Backup or Set Up as New iPhone. Since you have a back up, pick the relevant option (we'll discuss setting up as a new iPhone below).
6) Restore your new iPhone from an iTunes backup
Connect your iPhone the computer that you backed up your old iPhone to. iTunes will check that you want to restore from backup of set up as new. Select the Restore from this backup option. While the restore process is taking place the iTunes progress bar may pause, it may just need more time, so don't unplug your phone. When the restore process is complete your new iPhone will start up. Keep the device connected to iTunes to sync your music and other media files.
7) Restore your new iPhone from the iCloud backup
If your old iPhone is backed up to iCloud you don't even need to plug your iPhone into your computer, although you will want to plug it into a power source. It also needs to be on a WiFi network. In fact, it is possible to set up your new iPhone without ever plugging it in to a computer. When prompted to set up, choose "Restore from iCloud Backup," tap next, and enter your Apple ID and password. Select the backup of your old device and tap Restore. Wait until the device has finished restoring from the backup – this will take longer depending on how much data is contained in the backup and the speed of your internet connection. When the restore process is complete, your device will restart. If you want to sync data not contained in the backup (such as music, videos, apps, and so on) you will need to connect to iTunes. (That's unless you have iTunes Match set up, that will allow you to download music from iCloud when required, similarly you will be able to download for free any apps you have bought but don't appear on your device).
8) Non-iPhone users moving to a new iPhone
If you are moving from an Android, BlackBerry, or Windows smartphone to Apple's iPhone, it should be relatively painless, but you can make transferring your data to your new device easier if you set things up the right way to start with. Make sure things are set up correctly to start with and there will be minimum hassle later.
9) How to activate your iPhone if you are new to Apple
Unbox your iPhone and turn it on by pressing the On/Off switch. A welcome screen greets you, displaying a 'Slide To Set Up' slider that rotates between different languages. Once you begin the activation process, you're asked to pick your language and country, and whether you'd like to enable Location Services. This allows Apple apps (and third-party apps) to access your location via Wi-Fi networks and your GPS (Global Positioning System) location. Your iPhone then checks for any Wi-Fi networks in the area that your phone can connect to; if there aren't any, or if you'd rather use your cellular service, just tap the Next button. From here, you can set up your device as a brand-new phone.
10) How to transfer email, contacts and calendars to your first-ever iPhone
If you're using a Gmail account or other POP or IMAP-based account for mail on your smartphone, it's already syncing to a central server. You should be able to add that account to your new iPhone with few issues. Apple's iOS has automatic setup for those using Microsoft Exchange, Gmail, Yahoo, Aol, or Hotmail; you'll also be able to manually set up a POP or IMAP account for mail, LDAP or CardDAV for contacts, or CalDAV for calendars.
11) How to sync music and movies to your first-ever iPhone
Use iTunes on your Mac or PC to sync your music, TV shows, movies, and photos from your computer to your new iPhone. If your smartphone wasn't an iPhone previously you will need to get the data from your non-Apple device onto your computer and into iTunes. Once your music and movies are in iTunes they will be ready to sync with your new iPhone. Plug your iPhone into your computer, open iTunes, select your device from the left hand navigation, and choose the music and movies you wish to sync. If you have a big collection of media and limited space on your device you can create Playlists and set them to sync with your iPhone.
12) How to sync photos with your first-ever iPhone
To sync photos to your iPhone you will need to add them to iPhoto or Aperture (on a Mac) or place them in your Pictures folder (on a PC). The syncing of the photos takes place via iTunes. As above, you can select your device and then choose the Photos button before choosing which albums to sync.
13) How to sync non-iOS Apps
Unfortunately, you can't port any Windows or Android apps from your old device to your iPhone. It is often the case that you will find parallel versions of those apps on Apple's App Store though. Note that if you have purchased content through apps – for example Kindle books – you will be able to download an equivalent app to access the data, in most cases at least.
14) How to import contacts from a really old phone
If your phone has a nano-SIM card you should be able to transfer contacts. Copy all your contacts to the nano-SIM in your old phone then, once you've set up your new iPhone, you can copy those contacts by swapping out your iPhone's SIM card with your old nano-SIM and heading to Settings > Mail, Contacts, Calendars > Import SIM Contacts. Once the import has completed, eject your old SIM and put the one that came with the iPhone 5 back in its tray. If your phone has a SIM card that doesn't fit in the iPhone 5, but it comes with a USB cable for connecting it to your computer, you may be able to transfer your contacts (and your photos) by exporting them through software.
15) How to keep my old SMS and text messages
SMS and MMS logs are not transferrable, but you may be able to rescue them from oblivion. It's not a simple process, but you may be able to save them onto your computer. There are a variety of programs available for exporting messages from your smartphones - SMS Backup & Restore for Android is one option.
16) Now get to know iOS 7
Spend some time getting to know your new phone. Even if you are a long term iPhone user the recent update to the operating system could be a bit of a shock. Read this article for pointers on the top features in iOS 7. Alternatively read our iOS 7 for iPhone & iPad review for more in-depth information about using Apple's new iPhone operating system.