Aikido/Watch Others Practice
Learning Aikido is largely a process of watching others and trying imitate what they do. While this is a bit over generalized (verbal explanations are important, too), much of what you learn will come from seeing someone else.
To effectively watch someone, you must be physically able to watch. There are several factors to consider here. Let's start with sight lines. Often, Aikido classes are crowded. If you are sitting way at the back of the mat with several rows of people between you and the instructor, you might not be able to see what's going on. When the instructor calls a break to show a new technique, students quickly line up. Usually, the formal order of rank and seniority doesn't apply during the class. If you have the choice, sit in the front. Be polite, but pick a spot where you can get a good look at your teacher. If you find yourself further back, you might be able to shift left or right to see between people. Regardless, do what you can to get a good view.
If you are on the mat, you will usually be sitting when it comes time to watch. Sitting means seiza (link). Learning to sit in a seiza position causes your spine to be straight. It is a strong, centered position that encourages proper breathing. Correct posture allows to both watch and listen more effectively.
Paying attention to what's happening isn't as easy as it seems. There are distractions all over: noise off the mat, sunlight through a window, etc. Finding a position in which you can relax will help your concentration.
If you need glasses to see things at a distance, wear them. Glasses can be a real problem, especially during practice. If you cannot see with out them, you'll need to find a way to keep them on, since aikido often involves moving or touching the head. Some invest in sports glasses - goggles with prescription lenses. If you have a problem with your glasses, ask a classmate who wears them how they deal with the problem.
Watching Your Teacher
The person teaching a class usually teaches by demonstrating the technique with a more advanced student. In some traditions, demonstrations are done without any verbal explanations, so you;ll need to watch closely. There are several aspects of watching someone demonstrate to consider. How do the hands and feet move? How does the whole body move? Where does extension and blending come into play? When you are watching, you can try to take everything in at once (the geshtault) or you can focus on particular aspects of the movement. Usually, your teacher will demonstrate the technique several times - perhaps with variations. You might try to grasp the whole technique all at once on the first go, then focus on specific aspects on subsequent displays.
Often during practice, the teacher will wander around the class observing students at practice. They might interrupt one pair to demonstrate a correction or show them what's going wrong. If you are nearby, it is proper to stop and sit in seize to watch the teacher work with another student. Use good manners when it ends by bowing. Naturally, this must be balanced by practicing yourself. If you spent the whole class watching, you'd never get a chance to try it.
Watching Fellow Students
Usually, if you are participating in a class, you won't have much chance to watch your fellow students. Sometimes, though, when space is limited, the instructor will divide the class and have one part watch while the other practices. This is an opportunity to watch your fellow students practicing. You are watching for two things: people doing it right and people doing it wrong. If you see someone doing the technique correctly, picture yourself doing it that way. If it seems wrong, see if you can figure out what went wrong. A lot can be learned by watching others struggle with the same techniques you are trying to learn.
Watching a Test
Finally, you may find yourself watching an Aikido test one day. Maybe you are waiting your turn to test, or perhaps you're just there to show support for your fellow students. Regardless, watching someone else test, especially if they are more advanced that you, is a great way to learn. Test situations are more formal that regular practice sessions and often involve special bowing and protocols. These vary considerably between styles and schools, and watching a test is a good way to learn them. Students being tested will be asked to perform certain techniques. Obviously, they are trying to demonstrate them to the best of their ability. Watch closely to see how each student performs. Does one student have better movement, timing, or form than another? How are advanced students different than beginner or intermediate students?