I don't really know any API's unless you're willing to learn a new, little known, language. However I did take a game programming class last semester and know some of the basics. It sounds like you're at about the same point I was before I took the class.
Anyway the first thing you'll need is, as KYA said, a game loop. A method that get's called 60 or so times a second is good. Then just have that method update the objects in your game as needed. Though if you stop here and just do that you'll become overwhelmed quickly. So the next thing you should implement is...
A state machine. Think about what sort of states and sub-states your game will have. So like your title screen would be one state, the main menu would be another, actual gameplay would be another state (most likely with a handful of sub-states). Have something like an enumeration represent any possible state your game could have and then use a big case switch statement in your game loop to only update the objects needed in each state, including transitioning to another state.
One more thing I'd like to show you to make wrapping your head around everything that makes a game a little easier is the Model, View, Controller architecture. Basically what you want to do is divide the execution of your game into three roles.
- The Model, which will hold most of your game objects, and the methods that govern their interactions.
- The View, which will render a snapshot of the model at any given time. I recommend giving this it's own loop (draw loop) similar to the game loop I mentioned earlier.
- The Controller, which should be the main part of your application. Have it hold both game and draw loops, as well as the current state of the game. All your UI should be dealt with by the controller.
Make each of these an object and only have them deal with their assigned roles.
That should get you started. You'll have to look for tutorials on how to implement each of these in your language of choice, but at least now you know what to start looking for. Once you have your MVC, state machine and loops set up work on one state and role at a time.
Good luck and happy programming.