The mattress is queen size and resting on two chairs. The chair I sit on is between them. This keeps the mattress in place and also curves it slightly, providing extra absorption of background noise from the side. I use a headset microphone to further reduce noise.
There are specially designed booths used for podcasting from offices, using sound absorbent foam. However, a simpler setup, with an acoustic panel of the type used for office partitions, curved and mounted on wheels might work well in a shared office.