Can astronauts urinate while they're standing in space without getting themselves into too much trouble?
As Ernest mentions, on the ISS you pee into a hose so leakage is avoided. It is captured and filtered by the Waste Hygiene Compartment.
If you're asking what would happen if you didn't use a hose - yes, it would get messy fast. Any free liquid balls together and floats until it hits something, at which point it globs into an interesting surface which sticks due to surface tension.
Since your bladder gives some significant velocity to the liquid it would bounce all over the place unless you are careful to deposit it into some sort of contained volume. Astronauts in space suits use a form of fancy space diaper and so the liquid is immediate absorbed to avoid this issue. Honestly this is the best option if you don't have the high tech suction hose equipment.
My friend Suni giving a good tour: