Hi,
As Eric has linked you to the Trouble Shooting Doc I will point out some other things that might effect it before you even get that far.
The Article/Doc makes it clear your Date An Time (including Time Zone need to be sorted)
Your Contacts App > Card Menu > My Card needs to be showing your details
This has been an issue throughout iChat but is about having your Mac set up properly.
AS has been said higher up the Thread the Country/Region settings in the app and the Address Book need to match.
I have not proved a link between the Language and Text setting about Country/Region but I do like to keep mine the same.
There is no issue about the Keyboard selected.
If the Mac Firewall Is ON then in the Option Button pane needs to show the "Allow Signed Software" is allowed.
Also at least IMAgent needs to appear in the List
Stealth should not be on as it prevents Screen Sharing, Video and Audio Only Chat within the AIM and Jabber accounts in Messages.
In the System Preferences > Network the DNS info needs to be present.
If using Airport/WiFi then click the Advanced Button > DNS tab
This should list the DNS servers of the ISP at least (not just your Router (192.168.x.x) )
If required add a Public DNS server or two. (there was some circumstantial evidence early on that some DNS servers could not find the Apple iMessages Server)
If you are running Little Snitch or other similar Port and IP scanning apps then these need to allow not only Messages and IMAgent but several other support items.
If your Mac User account is subject to Parental Controls then they need to set up the settings for Messages including the iMessages account.
Other than the four errors quoted in the Linked Doc there are some other somewhat common in terms of issue reporting item that also occur.
One is the missing/disabled AppleGothic font issue.
I refer to this as issue 7 as it appeared after the one I list at number 5.
Number 5 Error message

This issue start in Messages 7 and continues into Mavericks at least.
It is an Account issue that affects only your Mac and the iMessages server.
Something happens to the iMessages server end that will not accept the login form your Mac.
It can only be reset by Apple Support Staff.
There is also number 6
This does not give you the error message above and you looked logged in but each time you try to send an iMessage then it reports the person is "Not Registered with iMessages"
With at least 6 symptoms with very similar outcomes it can be difficult to judge whether you are joining a thread about the same issue.
If when you check the things listed in the Apple Doc that Eric Linked you to then try a PRAM reset next.
Restart the computer holding down the CMD+ALT+P+R keys until you have heard three Start up bongs, then let the computer complete the start up.

9:32 pm Saturday; November 1, 2014
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad