I am going to be building my new home soon and am curious on how to limit my construction waste and how to properly handle that which will be produced. I would love to divert it all from the landfills, but I am sort of a novice here. If anyone knows how I should approach this and what to tell my contractor, that would be so so helpful.

Discuss your intentions with your architect/designer early on and also do the same with the contractor and as many subs as possible. Talking with the architect will help on the front end, ensuring that it is written into the plans and specifications that certain measures should be taken to reduce waste. An architect can also work on a design that minimizes waste as well.

I don't plan on having an architect. The builder I am working with is somewhat new to green construction and this hasn't come up in any conversations yet. It worries me. Should I just tell him that this is important to me? Will he charge me extra?

If you are paying him, then you should be able to tell him how you want things done. Its should be as easy as that. I would guess that he might charge more, but all in all, its not like you are asking him to do anything he is incapable of.

I agree with the above comments and would add the following:
The design of the home will drive the amount of waste generated to a large degree. For example something as simple as designing rooms and the overall size of the building to fall within full sheet sizes of sheeting and drywall. For example, people love bump outs. They look great! But a 1' or a 3' foot bump out will create more of a problem then will a 2' or 4'.
Careful ordering of lumber and reuse is important. For example, if 2 X 10's or 12's are used for concrete forms, buy with the idea of reusing them for window and door headers. Sure it will require a bit more care and clean up, but they come to the site and stay there are part of the structure.
The same can be done with temporary bracing of walls using 2 X 4's and reusing them as permanent lateral bracing in the attic on the trusses.

Choosing a designer up front and discussing how he will do this should help you make a good choice, then follow up with the builder in the same way. It truly is a team effort.

Just like some people don't like to make their bed in the morning, or pick up the dog poop in the yard, some of those same people design homes and build houses. It never hurts to drive by their business and home and take note of the care they use in their own surroundings. It can speak volumes!
;)