tl;dr In the ascent config, the suits were pressurized with pure oxygen to slightly above the cabin pressure. During ascent, the cabin pressure dropped from ~ sea level pressure to ~ 6 psia. The suit pressure control system vented gas to maintain the same slight positive pressure.
Before sealing up the suits, the crew performed a "prebreathe" to flush nitrogen out of their bodies. When the crew was suited up in the Suit Lab before launch, their suits were at 100% oxygen.
The hand-carried "ventilators" maintained a positive pressure of ~0.4 psi in the suits while traveling from the Suit Lab to the capsule. (source)
(Cropped and annotated from here)
In the capsule, pressure in the Pressure Suit Circuit (PSC) was controlled to slightly above cabin pressure (+.07 psi) by the O2 demand regulator.
Before the hatch was closed, the cabin atmosphere was sea level air. After the crew was 'installed' and the hatch closed, the cabin was maintained at slightly above ambient pressure. The crew was suited and breathing pure oxygen, the flow into the PSC was set to maintain a slight overpressure above the cabin pressure so that flow would only be out of the suit circuit into the cabin.
During ascent, when ambient pressure decreased below 6 psia, the cabin positive pressure relief valve opened and the cabin atmosphere started to flow out through it. The PSC bled down to maintain the slight overpressure through a valve in the O2 demand regulator.
All cabin atmosphere makeup gas was pure oxygen, so after most of the sea level atmosphere was relieved out during ascent, the cabin atmosphere would trend more and more toward pure oxygen. Eventually it would be ~5 psi of pure oxygen + metabolic contaminants.
Helmets and gloves were removed ~ 15 minutes after launch.
This environmental system schematic is still busy but it's better than the one in the Operations Handbook!
(Drawing from Apollo ECLSS Experience Report)
Suit absolute pressures:
- Traveling from Suit Lab to capsule: Ambient pressure (~15 psi) + ~0.4 psi
- At liftoff: Ambient pressure + slight cabin pressure increment + slight PSC increment
- After cabin blowdown during ascent: Cabin pressure (~6 psia) + slight PSC increment
Source: Apollo Operations Handbook
Some info from Crew Systems Division Apollo 11 postflight report