This is a good question, though a bit strange and it concerns me a little bit.

On one hand, it is a perfectly reasonable request for a manager to want to know what an employee is actually doing - after all, he/she is getting paid to do a job. On the other hand, the idea of trying to actually monitor what a remote worker is doing - to be sure he/she is working instead of sleeping or otherwise not working - is a bit unsettling to me.

The essence of telecommuting is that managers have to focus on the results and work products, not on the activity levels and sheer presence. So, to a certain extent it really doesn't matter whether the person IS sleeping or not, as long as he/she creates the desired end product on time and according to specification, e.g., a report, a budget, etc. This obviously varies a great deal from job to job - it's fine to focus on work products like that for someone like a technical writer or budget analyst, but not for someone taking incoming calls from internal or external customers, and who therefore doesn't have the discretion to NOT work at the assigned times.

The direct answer to your question is that as far as I know, there really is no way to actually monitor what people are doing. You can measure the times they log on and off the computer system, but it wouldn't take too long for a telecommuter to figure that out and (if they want) log on, go back to sleep for four hours, and then log off. Similarly, any attempt to measure keystrokes is subject to various kinds of abuse. And I suggest you not even consider any kind of visual monitoring such as by videoconferencing - that's a gross intrusion, in my view.

Keep in mind that one of the keys to effective telecommuting is careful selection of telecommuters. If you pick people whose work record and demonstrated skills/traits while working IN the office are very good, they are not likely to turn into a chronic sleeper while telecommuting. This is especially true since the telecommuter will know that the manager has a right to bring the person back into the office full-time if work performance suffers. So, I'd argue that nobody is as interested in doing a good job as is a carefully-selected telecommuter.