What test could I use to measure the short-term memory capacity of a group of people? I want to start a project about the best schedules for learning activities focused on college students.
Since sleeping patterns are totally different in a young adult/teenager, and many of the classes at my university start at 6:00 AM, I had the idea to measure the level of learning capacity or memory an individual between 17–20 years old can achieve at different hours of the day, and assess if it is actually affected by time of day. But first I need to know what kind of tests I could use for this study. 

What test could I use to measure the short term memory capacity of a group of "normal" people without any diagnosed learning difficulties?
There are several commonly used measures of Short Term Memory (STM). 


Memory span: lists of items are presented sequentially and the participant has to repeat each list after it ends. The lists become progressively longer. The most common variant is called Digit span, in which the items in the lists are spoken digits. Another common variant is called Backwards Digit Span, in which the participant has to repeat the list in backwards order. The WAIS test battery has an implementation of both, along with a standardized scoring method.
Free Recall: a list of stimuli (usually nouns) are presented. After the presentation ends, the participant has to recall, in any order, as many items as possible from the list. The list is typically, 10-15 items long. This task has been used for a long time (e.g. [1]) and is still used in current research (e.g. [2]). Note that there is another variant of the task that is called Serial Recall, in which participants have to recall the items in the order in which they were presented. This variant is essentially identical to the Memory span described above, except the lists used are usually of constant length, and not successively longer as in the memory span task.
N-Back: a stream of stimuli is presented, and the participant has to respond whenever the stimulus presented is identical to the stimulus presented N steps ago. N usually starts at 2, and increases as the participant performs better. This task has been used for a long time (e.g. [3]) and is still used in current research (e.g. [4]). 


You should also be aware of the close term Working Memory (WM). The distinction between STM and WM is not really clear. If there is such a distinction, STM deals with simply holding information in memory "As-Is", and WM deals with the ability to perform mental operations on it (such as comparison to other stimuli, mental rotation, re-ordering, etc.).
Backwards memory span and N-back are usually considered tests of WM, while forwards memory span and free recall are considered tests of STM.

As a side note: if you are interested in improving learning/teaching methodologies such as the schedule of classes, I'm not sure why you are interested in measuring STM. I would guess a more relevant property to measure would be the long term retention of what was learned.



[1] Murdock Jr, B. B. (1960). The immediate retention of unrelated words. Journal of Experimental Psychology, 60(4), 222.

[2] Farrell, S. (2012). Temporal clustering and sequencing in short-term memory and episodic memory. Psychological review, 119(2), 223.

[3] Kirchner, W. K. (1958). Age differences in short-term retention of rapidly changing information. Journal of experimental psychology, 55(4), 352.

[4] Jaeggi, S. M., Studer-Luethi, B., Buschkuehl, M., Su, Y. F., Jonides, J., &amp; Perrig, W. J. (2010). The relationship between n-back performance and matrix reasoning—Implications for training and transfer. Intelligence, 38(6), 625-635.