make all your objects black and allow the background to be white. This will help illustrator to separate the objects and ignore the background. Once the tracing is done, then you can set the colors to what you want.
You did not mention what version of illustrator you have as it has changed some, mainly the name of the tracing command
Once you open the png, make sure the image is selected, then you should find the tracing button in the top tool bar.
After the image has been traced, you can the see the tracing tools in the top tool bar, there you will find the preferences for tracing. Clicking it will allow you to choose between some presets, adjust the setting to your liking and the check box to ignore white.
When you are satisfied, you can then click the expand button in the top tool bar.
If you are still happy with it, use file>save as to save your vector file, preferably in the ai or pdf formats.
Next use File>Save for web or File>Export to save as a jpg or png either one can be used by your teacher. Keep in mind that jpg does not support transparency, if they plan on overlaying the objects over another file, png would be recommended.
Saying all that, keep in mind there are times when it is way better to trace manually using the pen tool. The auto tracing feature can add extraneous points that normally would not be required. Just keep that in mind.
It a fairly simple design with some none overlapping curves and some text. Anyway I have managed to find the tracer button. And I have e latest version. One thing you didn't cover their is this.
I would like the shirt to be black and white. So is it possible to change the lines color back once in vector or am I stuck with black forever?
Thanks for your help!
If you plan on printing white on a black tee-shirt, leave the colors alone. The text must be black and the background transparent or white. The printer will substitute white ink for anyplace that is black and will apply that ink to a black tee-shirt.
Actually it would be best to ask your printing service as they could have equipment that I never heard of or uses a new technology.