What is the ruling on studying how to clean and care for the face with the aim of working from home with clients?

There is no harm in studying or working in the field of cosmetology, provided that it is free from শরী‘আ (Islamic law) prohibitions such as intermingling with men, unlawful seclusion (khalwa), or practicing a forbidden act like plucking eyebrows, peeling the face, or anything that alters Allah's creation.