I have a friend who has a HAM license and a ham radio, and when he first pushes the button to talk, I hear a "call dialer" sound. It sound like someone is dialing a phone number in. The tone starts in the beginning of the broadcast, it sounds a phone dial tone 3 times, and the same at the end of his transmission. What is this? Thanks!
Between the clue in your original post ("sounds like someone is dialing a phone number in") and a more pertinent one in Joshua Nozzi's answer ("Maybe a shiny new Baofeng handheld?") that you seem to have acknowledged, my guess would be that Someone Who Isn't You® has accidentally enabled the Automatic Number Identification feature on the handheld:
In dispatch environments it's common to have a system in place that will allow radios to automatically identify themselves to the dispatcher. This is known as Automatic Number Identification (AIN), or sometimes PTT-ID since the radio sends a data burst containing the ID code at the beginning or end of a transmission. The Baofeng UV-5R uses DTMF signaling to enable ANI implementation.
The instructions there describe how to disable it via the PC configuration software, but IIRC it's also configurable through the menu via the handheld's own keypad.
Correcting my first answer after a re-read: It sounds like a "courtesy tone". I initially thought DTMF tones (like dialing a number) for accessig a repeater, but you mentioned "dial tone" (the steady tone on a land line before you start dialing) and it got me thinking it may just be a courtesy tone. More descriptive detaul would be needed. Or as Kevin said, you could just ask your friend.
Given your other recent question, however, I ask with a friendly grin if this "friend" is you trying to understand your radio before you're licensed by keying it a few times. Maybe a shiny new Baofeng handheld? ;-)
I'm sure it's a friend though. :-P
I'd be pretty willing to bet you have a Yaesu. Press the button that looks like an atomic symbol. It's used for digital modes, that are almost never used, and this is a frequent issue.