De-slecting units

I was grouping some units and when I wanted to add them to a different group they where still in the old one. How do I remove a unit from a group or make it so they are not in multiple groups?

i think you mean the shortcut keys rather than the physical groups of units on the map, which is the only way a unit can be in more than one.

for example: unit A B and C are assigned to shortcut #1 (using Ctrl and 1) units D and E are assigned to shortcut #2.
to reassign unit C from #1 to #2 u would have to select unit C alone (double click the unit itself or click its icon in the bottom control panel when the group is selected), then shift-select units D and E so u have all 3 selected, then hit Ctrl 2 to assign that group to shortcut #2.
u would then have to reselect A and B without C and hit Ctrl 1 to assign them to shortcut #1 (removing C).

to completely clear any shortcut key, eg shortcut #1, then hit escape so u have nothing selected and hit Ctrl 1, literaly assigning nothing to shortcut #1.

its actually a lot harder to put it into words than to do it, and is nowhere near as complicated as that explanation might make it seem. but i hope this helps.