I have previously written two posts on configuring iMessage, one with some help on setup and another with some updated details as Apple implemented revisions to the feature. Without wanting to repeat this information in detail I'll be going over a couple of specific points that will help you use iMessage, and have a consistent experience.
My first piece of advice is to check your iMessage settings on your iOS devices and any Mac's running Mountain Lion or later. There are two groups of settings under the heading 'Send and Receive'. If these settings are not identical on each of your devices then you may experience problems with conversations not syncing and with conversation threads splitting. If you are an iPhone user then my first real tip is to set 'Start new conversations from' (originally labelled 'Caller ID' in earlier iOS versions) to your phone number. This way, when you give someone your number they will automatically trigger iMessage if they have the capability, but also there will be no confusion from your messages to them suddenly originating from an e-mail address at a later time.
You can still give an e-mail address for the purposes of iMessage, and remember that a conversation should continue to use the contact details that it was initiated with. If a friend iMessages you by your email address, your responses will be from that email address. If you delete the conversation and start afresh however iMessage will use your default.
My second tip is to disable 'Send as SMS'. This will not disable normal text messages but will prevent failed iMessages from trying to send themselves as texts. This is potentially a costly option if you are abroad or if you are having a conversation with an international friend. When a message fails it will alert you with a red exclamation mark where you would usually see the unread messages count. Tapping a failed message will give you the option of retrying or instead sending the message as SMS.
My third 'tip', really more of a new feature highlight, is actually hidden in your e-mail settings. In 'Mail, Contacts and Calendar' options you will find a new set of settings under 'Short Name'. In here you can alter the way that names are displayed in iMessages (and other apps). If your contacts have nicknames assigned, then Messages can display the nicknames; although my Mother's contact details contain her full name, as her nickname is 'Mum' she appears as such. I think this is a pretty cool little detail, though I did end up removing some of my contacts sillier monickers...