How does one distinguish between, for example, 便宜 (cheap) and 便宜 (convenient) in written Chinese?
The context may give no help whatsoever, cf.
我的大学很便宜。
(Bad example, please excuse my awful Chinese. Feel free to edit with a better one.)
Is there a general rule for identifying which meaning is intended when there are identical characters?
Yes, this word has two different pronunciations.
便宜 pián yi means:
[adj] cheap, inexpensive
[noun] benifit, interest, which you are not supposed(allowed) to get.
[verb] to make sb get that benifit
便宜 biànyí means:
[adj]convenient
Because these meanings are different significantly, I don't think we'll get confused. Also, biànyí is a written, literature ,classic word, so you won't meet it in most cases. Instead, we'll use "方便" in that case.
In your example, I don't think 便宜 is used correctly, no matter how it pronounces. You may want to say:
我的大学学费很便宜。 The fee of my university is very cheap.
我的大学上网很方便。It's very convenient to surf the web in my university.
First, your example is bad. :)
Second, 便宜 (convenient) is not very commonly used. It appears almost only in set idioms such as 便宜行事 (meaning 'act as one sees fit'). If you see 便宜 alone, you can assume it means "cheap". You will be right 99% of the time.
Third, if you are looking for a general rule to distinguish between homographs, there is no simple easy rule. Your can use grammar and context to help you understand.
Fourth, there are times when homographs cannot be distinguished, and that is often intentional--punning. :)
In fact there is only one important meaning of 便宜（cheap）。 when we want to say something which is convenient we say 方便。
I don't think there is a general set of rules beyond what is obviously distinguishable by grammar (e.g. "Can it be used as a verb here?"). Your only tool is context, and there is nothing universal about context.
