Skype Mobile is now available to all Android phones owners with any carrier.

Skype Mobile which until now was only available to Android phone owners using Verizon Wireless in the U.S., is now open to anyone owning an Android phone on any network. The only requirement is that the phone has Android 2.1. With Skype Mobile, users will be able to make calls using 3G networks and Wi-Fi worldwide and Wi-Fi only in the U.S. The new app also allows all Android users to send and receive IMs through Skype for free, and hold conference calls with other Skype users for free. Charges apply when you start to use the app to include or call numbers that aren't Skype users according to AppScout.
Still according to AppScout, "current Skype users will be able to pull down their existing contact lists, and place calls to other Skype numbers for free." If you want to call non Skype users, you'll have to sign up for a calling plan or pay as you go. You'll have to sign up for a calling plan or pay-as-you-go if you plan to call non-Skype numbers, like traditional land-line telephones and other mobile phones. You'll also pay to receive calls to your Skype number from people who aren't using Skype.
The new Skype app also allows you to synchronize names and numbers between your Android phone's native contacts list and your Skype Address Book, so you can place calls to your friends using the Skype app back at your computer as well and vice versa. Instead of managing two contacts list, Skype combines them.

Watch here a demonstration of the app:

For more, see AppScout.com

Using Skype mobile on your cellphone.

As it continues to grow, Skype, which offers telephone services for free or nearly free to users via VoIP or voice-over-Internet protocol through their computers, has expanded its service into the mobile phone arena. Even before Skype made the move, other companies were already offering software that allowed certain phones to work with Skype.
The Skype software for mobile is available free for smartphone like the iPhone, Samsung, Nokia, Windows and Android phones etc, and other devices like the iPod Touch, Sony PSP etc.
With these various devices, Skype offers different levels of services and connectivity. But in general, Skype mobile works under the same principle as the one on computers by allowing users to make calls and send instant messages to other Skype users free, and pay lower rates than the ones from the phone companies when calling landlines or other mobile phones.
There are other restrictions like the one imposed by Apple to only allow Skype mobile calls to be made through WI-FI connection and not over the network of its carrier partners like AT&T.

For more, see NYTimes.com