Going back to university after suspension, how do I move past the shame? I was suspended for 1 year from my university for copying an assignment from an online source. There were several extenuating circumstances but I won't go into them as they are irrelevant, I did cheat and I do deserve the punishment I was given - that is not the question. 

After I found out my sentence, I found it very hard to attend classes relating to that department, or to look professors or my deans and advisors in the face and carry out conversations with them. The professor who's class I cheated in is one I was hoping to talk to as she is in the same area that I hope to go into one day and I really enjoyed her class, teaching methods, and enthusiasm for the subject. I also am extremely saddened by the fact that since I'm a fourth year, this means all my peers will be graduating and will have left by the time I come back and I'm finding it hard to cope with the thought of being without them for the rest of my undergraduate career.  

My question is how do I cope with the stress and shame I am feeling and how do I get over that so that I can return to the academic environment in 1 year? Can I ever approach that professor again, or should I avoid her? I'm asking this here because I'd like the opinions of those who are on the other side of this.
The university suspended you, which is a signal that it is still willing to have you as a student after serving your suspension.  (If it wasn't, you'd have been expelled.)  Therefore, upon your return, this professor (and every other professor) has the same professional obligations towards you that she would to any other student: to accept you in her classes, to treat you with courtesy and respect, to help you learn the material, to grade you fairly based on your work and the standards of the course.  It is possible that your assignments may face extra scrutiny for plagiarism, but hopefully that is irrelevant as you're not going to do it again.

It's possible that relations may be strained between you, but I think this may be more on your side than hers.  Speaking for myself, I certainly find it disappointing when a student cheats, but it's not as if I'm going to declare a personal vendetta against them and seethe with fury every time I pass them in the hall.  That would be unprofessional, and not worth the emotional energy anyway.  We go through the disciplinary process, I hope that they learn their lesson, and it's back to business as usual.  If they are able to turn things around and show genuine interest in and dedication to their studies, for me that's ultimately uplifting.

So if you want to take her class at a later date, by all means do so.  You might find it helpful to talk with her first: express your regret over the incident, as well as your continued interest in your subject and in completing your degree.  I think it's very likely this will help clear the air for both of you.  It would be wise for you to be extra diligent about quotations, citing sources, etc, and to consult your professor if you have the slightest question about any such issues.

Maybe she won't invite you to dinner, and she probably won't be the best person to write you a letter of recommendation.  (Even if you get to be on better terms, which I hope you will, she might still feel it's her duty to mention the cheating incident in any letter she writes, which is probably not good for you.)  But I don't see any reason you can't have the same basic educational experience as any other student.