Gordon Cooper, one of the first 7 astronauts recruited by NASA in 1959, pose in his Mercury suit, the same one used in 1962 by John Glenn, the first American to go into orbit around the Earth.
The Mercury suit was not a real space suit: it was actually a modified version of the Mark-IV pressurized flight suit, used by US navy pilots for high altitude flights.
Designed to be comfortable for long periods of time – the astronauts of the time did not have the possibility to change themselves on board – it was equipped with the main survival systems: it provided its “inhabitant” with oxygen for breathing but also pressure in case of depresurization of the cabin. However, this clothing did not allow any type of extra vehicular activity such as spacewalks.
After the first flights and the first landings it was equipped with floats that allowed the pilot to leave the cockpit in case of post-return problems.
And if you’re wondering how astronauts did their needs, since the spacecraft of those years didn’t have a bathroom, the answer is … in a diaper. NASA