Wikivoyage tells you all you need to know -- and I'm going to quote most of it, since I originally wrote the entry!
Don't panic — help is at hand. The first key to solving the puzzle is
that the actual flush mechanism is usually not operated by the control
panel: instead, there is a standard, familiar, Western-style lever,
switch or knob somewhere and it is thus entirely possible to take care
of your business without ever using the washlet features. (In rare
cases, mostly with very high-end gear, flushing is integrated; if
lifting your bottom off the seat doesn't do the trick, look for
buttons labeled 大 or 小, meaning a big or small flush respectively, on
a wireless control panel on the wall.) The second key to exploration
is that there is always a big red button labeled 止 on the panel —
pressing this will instantly stop everything. Older models simply have
a lever nearby that controls the flow of a sprayer.
Armed with this knowledge you can now begin to dig deeper. Typical
controls include the following:
Oshiri (おしり) - "buttocks", for spraying your rear - typically shown in blue with a stylized butt icon; this action can be unnerving,
but travellers should not be afraid - by the second or third attempt
it will seem normal
Bidet (ビデ) - for spraying your front - typically shown in pink with a female icon
Kansō (乾燥) - "dry", for drying off when finished - typically yellow with a wavy air icon
Other, smaller buttons can be used to adjust the exact pressure,
angle, location and pulsation of the jet of water. Sometimes the seat
of the toilet is heated, and this can be also regulated. One
explanation is that since houses are not usually centrally heated, the
toilet business can be made a little more convenient by heating the
seat. To be polite and save energy, you should leave the cover down on
heated toilet seats.
And if that wasn't enough, Wikipedia tells you way, way more than you need to know.