iOS: (Make sure you have iTunes installed!)
Step 1: Download and open Cydia Impactor.
Step 2: Download PyChat's IPA file.
Step 3: Connect your device to your PC, verify it appears in Cydia.
Step 4: Drop the .IPA file into Cydia, and follow the instructions on the screen.
If it complains about invalid Apple ID credentials, go to https://appleid.apple.com and generate an app-specific password.
Step 5: Go into Settings -> General -> Device Management and tap on your email. Press "Trust" at the top.
Done! You should see the app on your home screen now. If you have any issues, let me know.