Tap Record a new greeting. Note: If necessary, delete an existing greeting (limit of 2 greetings) to make room for the new greeting: Tap the Menu key, tap Delete greetings, tap the check box next to the desired greeting, and then tap Delete.
My iPhone always seems to jump to voicemail before I answer it. I need to increase the call forward delay. By increasing the delay before the call is transferred to voicemail, I have a better chance of grabbing it. As expected, the caller will hear an increased number of rings before being transferred.

Open Settings → General → About → If there is an update, you will see a pop-up. → Tap Update.
Before you push record, be sure to tell the person on the other end of the line you're recording; depending on your location, you may be breaking a law if you don't. Some US states—like New York and even the feds—only require one-party consent, which means you can record without telling the other person or persons. In California, all parties must know they're being recorded—even if the recorder is out of state. Under federal law, one-party consent is okay, but only if you're part of the conversation; otherwise that's considered eavesdropping.