Armour through most of the medieval period consisted primarily of chainmail with the only real plate armour being helmets. In that case, relieving yourself is a straightforward matter of lifting your maille. We even have entertaining depictions of this happening: https://pin.it/3hxHb8N

As plate armour developed from the mid 13th century onwards, it began as simply reinforcements added overtop of maille, such as a coat of plates for the torso, gauntlets for the hands, etc. None of that really changes the way going to the washroom would work in practice.

By the mid-late 14th century plate armour began to reach a more developed level, we start to see cuirasses take the standard form of a breast and back plate attached to a fauld, which would hang down from the natural waist down to the crotch. Typically soldiers would wear a maille skirt underneath for added protection. Since a fauld covers the mid section of your body, it is designed to collapse vertically to allow you to hinge at the waist for maximum mobility. This allows the wearer to simply hike it up along with the maille skirt in order to relieve himself just like his ancestors.

There are two main instances down the line as we get into the 15th and 16th centuries, where things change a little bit. Around the mid 15th, especially in Germanic areas, something called a maille brayette came into common use. These are essentially chainmaille underpants that fully enclose the groin. In this case, the wearer would be slowed down a little bit, but they would only be required to unhook two small hooks to remove the mail in order to go. We also run into steel codpieces which would present similar problems, but which could be easily removed by a strap, possibly with the help of a page.

The other exceptions are sort of a broad category of mostly tournament armour features which one way or another enclose the crotch in plate. We have a few examples of intricately articulated crotch and butt plates, the most famous example being Henry IIX unused tournament armour from the field of cloth. There are also a few extant French examples as well as some earlier examples surviving in German art. Another example is the type of armour Henry actually ended up wearing to the field of cloth tournament, a tontlet armour. A tontlet is much like a fauld in form, except it extends much lower, looking much like a ball gown, making it impractical to lift it out of the way for either horse riding or bowel vacating (although some actually had removable cutouts pinned on to make it possible yo ride a horse)

In either of the above cases, the wearer would need to either go before they get dressed (practical in a tournament, if not on campaign), or else get the assistance of their team of pages to get undressed enough to take care of business.