I just recently recieved a peice of music (Sonata for Trombone and Piano. by Eric Ewazen)from my private instructor and it has Tenor clef on it. I know how to transpose it, but I would much rather know it that have to write in all the notes. My band director told me that it wouldn't be worth my time to learn it. But I kind of want to. Does anyone know what I should do, or how I should go about learning Tenor Clef?

Fortunately, the Ewazen Sonata isn't entirely in tenor clef... But I have to disagree with your teacher that it is a waste of time to learn. Think of the situation you are in now. You have a piece you want to play, and can't read it. Personally, I'd never want that to happen again. Now.. if you just want to play in middle school and high school and don't intend to audition for all state/regionals... then I guess you don't really need it. But if you intend to stay with trombone, it's something we all should know. Alto clef??? Not so much unless you have orchestral ambitions.
For example, go to this site and click on the audition requirements for the upcoming audition for the DC Navy Band. You'll notice four out of the eight pieces have tenor clef.
http://www.navyband.navy.mil/auditions.shtml
I hate nothing more than getting with a group of players to play quartets or something, I have a new piece I am passing out and a guy goes "uh oh, I can't read tenor clef".. It's very frustrating.
As for how to learn.. you will get varied replies, but a book I have found to be a great start is "Introductory Studies in Tenor and Alto Clef for Trombone" subtitled "Before Blazhevich" by Brad Edwards available at www.hickeys.com
It's very well paced and really helps ease you into it. While your at it check out his book of lip slurs too.. great stuff.

i know a very limited amount of tenor clef, but with that limited amount I was able to join a local brassband. But I also agree that its NOT a waste of time just because of exactly what steve said, but I hate being that person or/and looking at a solo piece and putting it back down. I hate that but I havn't learned it because of the lack of need/time to do it. Hopefully one day, but its somewhat needed in my opinion.

The key is to NOT wait until it shows up... learn it now. Make the time. Five minutes a day allotted in your routine will make a huge difference.

Absolutely learn tenor clef. I'm a bassoonist, but my son is an 8th grade trombonist (1st chair in all state). His band director (also his private teacher) has him working in "Introducing the Tenor Clef for Trombone" by Reginald H. Fink. My only problem with this text is that the studies are in LOW tenor clef (in the lower register) until it throws him in the deep end in excerpts.

Reading within the clef for me is more visual. Because I transpose when playing flute and alto flute, I look at the note, but I see a "ghost" note a 5th above. Of course, I get above the staff, I just KNOW those notes.

Find the method which works best for you ... learn it like you did with bass cleff (find a device - DFACE ... Dogs Find All Cats Edible for lines, for example), or like I do ... "see" the note a 5th above until you get the hang of it. But whatever method you use, LEARN TENOR CLEF.