How to Reinstall Cydia

Method 1 of 2:

Go to the official Redsn0w website at http://www.redsn0w.us/2010/03/download-direct-links-jailbreak-guides.html.
Select the option to download and install Redsn0w to your computer.
Launch the Redsn0w application after installation is complete.
Connect your iOS device to your computer using a USB cable.
Select the option to 'Run' Redsn0w from within the application, and place a checkmark next to 'Install Cydia.'
Click on the 'Jailbreak' button.
Wait for Redsn0w to inform you that Cydia has been successfully installed on your iOS device.^{[1] X Research source}

Method 2 of 2:

Launch Safari on your iOS device.
Enter the following URL into the address bar of Safari: http://apt.saurik.com/debs/cydia_1.1.8_iphoneos-arm.deb. This link will allow you to install Cydia directly on your device without having to use a computer or other third-party applications.
Select the 'Install' option offered by iFile, and wait for Cydia to complete installation.
Close and restart the iFile application. Cydia will be reinstalled on your iOS device.^{[2] X Research source}