Having just started back on Monday after a 15 year absence, I might have a suggestion or two :-)
Aikido takes time. I remember practicing the most basic technique (tai no henko) for months (six days a week) before I had my first "ah" moment. Not that I understood the technique, I just finally understood a very small part of the technique.
Learn your ukemi and practice it constantly. If other students arrive early, ask them to help you. Better ukemi means less injury.... IMHO. Better ukemi also means that higher ranked students are more than happy to practice with you at any time....they can execute the technique with full power and know that they won't hurt you. And practicing with higher ranked generally means you will learn faster.
Practice what you can outside of the dojo....standing in hamni, sitting in seiza, stretching the wrist tendons, etc.
Practice inside the dojo....clean the mat, do what you see needs to be done, ask how you can help. If you don't know etiquette, ask. If you don't know how something is done, ask. If you don't know someone, ask....
Bring paper and pen to class, and after class, ask a sempai the techniques practiced that night. This will help you learn the terminology and get it locked into your mind. Keep an aikido journal of your practices, including techniques, and anything you noticed that you need to work on, as well as anything that others pointed out to you. Believe it or not, you will learn techniques faster, because you will be able to associate the name of the technique with what is actually being done.
Other than that, have patience and have fun!
Welcome to aikido!