It is of course, a lot easier to clean with the machine powered off. If you overdo the liquid, things can be left to dry out. Never use much heat to do this, though an airing cupboard would be ideal.
For both screen and keyboard I use washing up liquid. Readily available. The liquid soap from the Gents when in an office works just as well.
For the screen, a dab on a damp (NOT wet) paper towel will clean the surface. Wipe over with a dry paper towel to avoid streaks.
Keyboards trap things like crumbs. A vacuum cleaner with an upholstery attachment can extract much of this stuff. Just make sure it isn't powerful enough to suck the keytops off!
The keyboard has crevices, which makes it more awkward. Forming the damp paper towel into a sort of wedge works. It's a bit of a faff, because there are a lot of crevices. Depending on the design, an old toothbrush, used virtually dry, can be used. I keep a stock of cheap toothbrushes from the Pound Shop for various small cleaning tasks.
Often, when I've had to visit a user's PC and noticed that the keyboard was filthy, I've examined the keyboard on my desk and been reminded that some time has elapsed since it had its own cleansing.
