What you are attempting to do is very, very difficult. SLAM is far from a "solved problem". For your small robot, you have a variety of tasks to perform, but it is difficult to say what they are because you haven't really described what your "maze" is going to look like. I have to assume that since you are using an ultrasonic sensor, that you are wanting to have a real maze with walls, correct? Have you built this maze yet?
You need to learn how to get your robot localize itself within that environment. By that I mean, from the robot's experience within the environment, it should be able to take sensor readings and then use that to determine where it is positioned at that moment in time within the environment. Once it knows that (and knows the destination of the goal), you then need to do path planning. Depending on the environment (whether it is a regular grid or not), this path planning can take the form of a discrete algorithm (like the wavefront algo or A*), or it might have to use a continuous algorithm of some sort.
Your robot will also need to be able to sense and understand how far it has gone from one point to another (wheel encoders and the like), along with what direction it is facing. Also note that since such sensors and methods are far from perfect, you are going to have some error in your sensor readings; with that in mind, you need to be able to adjust for this error, and use it to factor in a probabilistic manner your algorithms so that your robot has a sense of not only where it is positioned and how it is oriented in the maze, but to also what degree it believes that it is correct.
I am not an expert on this - far from it. I am merely telling you what I know from what I have read online, as well as what I have learned in the past 4 weeks or so taking the Udacity CS373 class:http://www.udacity.com/overview/Course/cs373/CourseRev/apr2012
This is -not- an easy class, but it will give you more than enough info to get you on your way with your project, though I am not sure whether you have the mathematical knowledge yet to be able to understand some of the material (exposure to linear algebra and probability/statistics is helpful).