Connect the Time Machine backup drive to the iMac. If you've never started up the new iMac, then when you do you will enter the Setup Assistant where you can opt to restore from a Time Machine backup. Just follow directions.
If the iMac has already been through the Setup Assistant, then open Migration Assistant in the Utilities folder and use it to migrate from the Time Machine backup drive.
A Basic Guide for Migrating to Intel-Macs
The Knowledgebase article Intel-based Mac: Some migrated applications may need to be updated refers to methods of dealing with migrating from PowerPC chips to Intel with the Migration Assistant safely. The authors of this tip have not had a chance to verify this works in all instances, or that it avoids the 10.6.1 and earlier Guest Account bug that caused account information to get deleted upon use of the Migration/Setup Assistant. However, a well backed up source that includes at least two backups of all the data that are not connected to your machine will help you avoid potential issues, should they arise. In event it does not work, follow the steps below.
If you are migrating a PowerPC system (G3, G4, or G5) to an Intel-Mac be careful what you migrate. Keep in mind that some items that may get transferred will not work on Intel machines and may end up causing your computer's operating system to malfunction.
Rosetta supports "software that runs on the PowerPC G3, G4, or G5 processor that are built for Mac OS X". This excludes the items that are not universal binaries or simply will not work in Rosetta:
1. Classic Environment, and subsequently any Mac OS 9 or earlier applications
2. Screensavers written for the PowerPC System Preference add-ons
3. All Unsanity Haxies Browser and other plug-ins
4. Contextual Menu Items
5. Applications which specifically require the PowerPC G5 Kernel extensions
6. Java applications with JNI (PowerPC) libraries
See also What Can Be Translated by Rosetta.
In addition to the above you could also have problems with migrated cache files and/or cache files containing code that is incompatible.
If you migrate a user folder that contains any of these items, you may find that your Intel-Mac is malfunctioning. It would be wise to take care when migrating your systems from a PowerPC platform to an Intel-Mac platform to assure that you do not migrate these incompatible items.
If you have problems with applications not working, then completely uninstall said application and reinstall it from scratch. Take great care with Java applications and Java-based Peer-to-Peer applications. Many Java apps will not work on Intel-Macs as they are currently compiled. As of this time Limewire, Cabos, and Acquisition are available as universal binaries. Do not install browser plug-ins such as Flash or Shockwave from downloaded installers unless they are universal binaries. The version of OS X installed on your Intel-Mac comes with special compatible versions of Flash and Shockwave plug-ins for use with your browser.
The same problem will exist for any hardware drivers such as mouse software unless the drivers have been compiled as universal binaries. For third-party mice the current choices are USB Overdrive or SteerMouse. Contact the developer or manufacturer of your third-party mouse software to find out when a universal binary version will be available.
Also be careful with some backup utilities and third-party disk repair utilities. Disk Warrior, TechTool Pro , SuperDuper , and Drive Genius work properly on Intel-Macs with Leopard. The same caution may apply to the many "maintenance" utilities that have not yet been converted to universal binaries. Leopard Cache Cleaner, Onyx, TinkerTool System, and Cocktail are now compatible with Leopard.
Before migrating or installing software on your Intel-Mac check MacFixit's Rosetta Compatibility Index.
Additional links that will be helpful to new Intel-Mac users:
1. Intel In Macs
2. Apple Guide to Universal Applications
3. MacInTouch List of Compatible Universal Binaries
4. MacInTouch List of Rosetta Compatible Applications
5. MacUpdate List of Intel-Compatible Software
6. Transferring data with Setup Assistant - Migration Assistant FAQ
7. OS X Lion: How to use Migration Assistant to transfer files from another Mac
Because Migration Assistant isn't the ideal way to migrate from PowerPC to Intel Macs, using Target Disk Mode, copying the critical contents to CD and DVD, an external hard drive, or networking will work better when moving from PowerPC to Intel Macs. The initial section below discusses Target Disk Mode. It is then followed by a section which discusses networking with Macs that lack Firewire.
If both computers support the use of Firewire then you can use the following instructions:
1. Repair the hard drive and permissions using Disk Utility.
2. Backup your data. This is vitally important in case you make a mistake
or there's some other problem.
3. Connect a Firewire cable between your old Mac and your new Intel Mac.
4. Startup your old Mac in Transferring files between two computers using FireWire.
5. Startup your new Mac for the first time, go through the setup and
registration screens, but do NOT migrate data over. Get to your
desktop on the new Mac without migrating any new data over.
If you are not able to use a Firewire connection (for example you have a Late 2008 MacBook that only supports USB:)
1. Set up a local home network: Creating a small Ethernet Network.
2. If you have a MacBook Air or Late 2008 MacBook see the following:
a. MacBook (13-inch, Aluminum, Late 2008) and MacBook Pro (15-inch,
http://support.apple.com/kb/HT3224;
Late 2008) - What to do if migration is unsuccessful;
b. MacBook Air - Migration Tips and Tricks;
c. MacBook Air - Remote Disc, Migration, or Remote Install Mac OS X and
http://support.apple.com/kb/HT3224; wireless 802.11n networks.
Copy the following items from your old Mac to the new Mac:
In your /Home/ folder: Documents, Movies, Music, Pictures, and Sites folders.
In your /Home/Library/ folder:
/Home/Library/Application Support/AddressBook (copy the whole folder) /Home/Library/Application Support/iCal (copy the whole folder)
Also in /Home/Library/Application Support (copy whatever else you need including folders for any third-party applications)
/Home/Library/Keychains (copy the whole folder) /Home/Library/Mail (copy the whole folder) /Home/Library/Preferences/ (copy the whole folder) /Home /Library/Calendars (copy the whole folder) /Home /Library/iTunes (copy the whole folder) /Home /Library/Safari (copy the whole folder)
If you want cookies:
/Home/Library/Cookies/Cookies.plist /Home/Library/Application Support/WebFoundation/HTTPCookies.plist
For Entourage users:
Entourage is in /Home/Documents/Microsoft User Data Also in /Home/Library/Preferences/Microsoft.
Credit goes to Macjack for this information.
If you need to transfer data for other applications please ask the vendor or ask in the Discussions where specific applications store their data.
5. Once you have transferred what you need restart the new Mac and test to make sure the contents are there for each of the applications.
Written by Kappy with additional contributions from a brody.Revised 5/21/2011
