Among carriers, the ways to access your voice mail from a cell phone or smartphone can vary. Typically, there is a pre-set speed-dial or pull down option called "Voice Mail" to keep it quick and easy. But, as is so often the case, there can be more than one way to skin the cat.
For example, holding down the number 1 on your phone's keypad (even if that is the touch screen of a Smartphone) may do it (generally works on Verizon devices), dialing *86 is also a common shortcut. And, with both Verizon and AT&T devices (including a BlackBerry), we've found simply dialing your own number from that phone can send you directly to the "please enter your password" prompt.
Remember when dialing your own number from your home phone resulted in a busy signal? What, a busy signal? Who even remembers those anymore? In this as in so many other things, today's mobile phones are a far cry from the analog ancestors they threaten to replace.