Having beautiful nails is all about caring for them. Nails need to be moisturised, especially after removing your nail polish. The cuticles are to be given strong protection else they might get easily infected. If you still want to remove the cuticles, do so after a shower or bath.
For healthy nails, when visiting a saloon, make sure the below items are in tact:
Check if the nail technician washes hands between clients.
Do not mind asking them as how they clean their tools.