Requirements
you need a call to action that attracts the user - so this should take the form of a message and/or image/icon that affords some interaction - eg an information icon, question mark icon, magnifying glass, basket icon, directional arrow, or something in context for your application.
It should be a self contained area (eg not blending in with surroundings) but not look too much like a standalone button because the user will too much expect to be able to click on it - there's needs to be a subtle undertone that says this is active but it's not a button, otherwise the 'this-is-a-button' thought will be too prominent.
The hover action should activate immediately - not wait for two seconds like many tooltip style help texts. This also aids accidental discovery as the user passes their mouse over, and dispels any further 'this-is-a-button' thoughts
Don't use the mechanism everywhere as the instant actions on hover really do get annoying when they pop up all over the place. Restrict instant hover to specific areas of interest.
The popup should hide as soon as you move outside its own space, - not the space of the original area that activated the popup.
If possible, try and indicate what is going to happen, for example show a 'cut-off' snippet of the content so that it really looks like something is going to move out or be exposed, or an arrow coming out from the edge of an area to indicate you're going to pull out a page or popup.
Examples
Typical scenarios that combine these steps are found on:
- ecommerce sites - eg for product details - basket price/list - all transient details
- web forms to get help on each item
- navigation menu items
Here's an example on a carousel (at the time of writing used at johnlewis.com online shopping site)

There's a clear call to action, it's obvious what is going to happen because of the arrow and the half hidden content on the popup, the hover action is immediate, there's no other interactive content nearby, and the popup goes away as soon as I move away from it.

Extremes
For an extreme example of use of hover - try looking at dontclick.it/ where after the first page ALL interaction is done with hover and no clicks are required at all.
I've also seen interesting behaviour that start to gradually fade in a small information panel as you start to move the mouse nearer to the hover object (within some maximum distance), so that you don't actually have to hover over it exactly before you start to see the panel. That may take a little trial and error to get right for a given scenario and it kind of relies on the hover object being somewhat separated from the main content or other areas of interaction. Unfortunately I can't remember where I saw that. Testing would be essential with that concept!