For this process, you should leave your computer in the same room as the Time Capsules, or use one Ethernet cable to connect your Mac to the Ethernet port on the existing Time Capsule, then use another Ethernet cable to connect from the existing Time Capsule to the new Time Capsule.
1) Configure your Time Capsule for your network. See the documentation that came with your Time Capsule for information about setting it up on your network.
2) Open Time Machine preferences in System Preferences.
3) Slide the Time Machine switch to Off.
4) Mount both Time Capsules on your Mac and open a Finder window for each of them by double clicking on each one. Take note of the free space available on your new Time Capsule.
5) Drag your backup disk image from the current Time Capsule to the new Time Capsule. This can take some time to complete because your entire backup will be copied.
6) Open Disk Utility (in /Applications/Utilities).
7) Drag the backup disk image from your new Time Capsule to the Disk Utility window. Once completed, the disk image will appear in the device pane on the left of Disk Utility.
8) Highlight the disk image in Disk Utility and click "Resize Image" on the toolbar.
9) In the "New Size:" field enter the amount that equals the free space of the new Time Capsule you noted from above, then click Resize.
10) Double-click your backup sparse bundle in Disk Utility to mount it.
11) Click the "Partition" tab.
12) Drag the partition size divider down to the bottom of the "Volume Scheme" (to make it larger).
13) Click Apply, then click Partition. This will expand the size of your backup sparse bundle.
Tip: You can use Disk Utility to check the integrity of the backup sparse bundle: highlight the backup sparse bundle, then click the First Aid tab. Click "Verify Disk" to check the sparse bundle.
14) Go to Time Machine System Preferences.
15) Click "Select Disk...", then select your new Time Capsule.
16) Perform a Time Machine backup.
17) After the back up, you can remove the Ethernet cables if desired and configure your wireless network to your liking.