Urinals tend to become blocked by calcium buildup rather than foreign objects. This can make them extremely challenging to clear of blockages. They also have smaller, narrower traps than toilets. This makes it easier for anything that does get down there to clog the pipe. The best results are obtained by pouring a product designed to dissolve calcium down the drain then using a urinal snake to take care of anything that's left.
Remove drain trap with a screwdriver to gain access to the drain.
Mix acid and water according to manufacturer's instructions and pour down the open drain. Wait to see if the drain starts to clear. If it doesn't, vacuum out the water.
Run the snake down the drain by placing the end of the snake at the drain entrance and turning the handle. Let it go down at its own speed as you crank. Do not try and force it down the drain, as you may break the urinal.
Reverse the crank when you hit an obstruction, pulling the clog back towards you. Again, do not try to pull or force the snake. Repeat the process until the clog is cleared and the drain is running normally.