Here is a schematic of the shower system.
A description from here.
This is an enclosure which uses continuous airflow as a gravity
substitute to move the water over the crewman. A 6-pound capacity
water bottle is filled from the waste management compartment water
heater, pressurized with nitrogen, and attached to the grid ceiling at
the shower location. The nitrogen gas pressurant expels water from
the bottle through a transfer hose and a crew- operated hand-held
spray nozzle. A soap dispenser provides the crewman with 8 milliliters
of liquid soap for each shower. During the shower this dispenser
fastens to the ceiling with Velcro. A suction head removes water from
the crewman and the shower interior. The suction head is connected
by hoses to the centrifugal separator, which deposits the waste water
into a collection bag. A blower pulls the air from the separator
through a hydrophobic filter that protects the blower.
Jack Lousma commented in a official document recording the results of a project which sought to learn from Skylab experience to help the ISS design:
You had to mix water in a 3-quart container – so much hot, so much
cold. You had soap that was probably better used in a veterinary
practice, because it made you itch. We sprayed water on ourselves
with a sprayer and then had to vacuum it off with a suction device.
One thing worth noting is that we were in this low-pressure
environment and so whenever you got that water on you and went to dry
yourself off, it got extremely cold because it was evaporating so
rapidly. It took a lot of vacuuming to get all of the water out from
inside of cylinder. You had to use a lot of towels to get dry.
During our mission we usually just took sponge baths every night with
a washcloth and a towel.
Well, I took a shower every 10 days whether I needed it or not. But I
found the shower to be quite refreshing and I enjoyed it. The only
downside was that it just took too doggone long to do all that stuff.
So if they can find a way to take a shower a little more quickly,
they’d be on the right track.
The average time for a shower was about 1 hour. You can clean up with
a wash cloth in 10 minutes or less. To me, I would skip the whole
thing. You don’t need a shower, even on ISS.
Their comments are summed up in the NASA document "Skylab Lessons Learned as Applicable to a Large Space Station" as
It worked in orbit, but, to the surprise of the author, many of the
astronauts did not feel it was required nor needed. Because of the
time to operate and clean up, few of the crewmen thought it worth the
effort. Future systems should be simpler to operate.