teacher(n.) 教师、教员(以教书为职业的人)
Teacher is the general term for someone whose job is to teach. There are many kinds of teachers, primary school teachers, high school teachers and university teachers.
For example:
I'd like to go into teaching and get a job as a teacher in an inner city primary or secondary school.
lecturer(n.) 大学讲师、讲课者、授课者
A lecturer is someone who gives a lecture or formal presentation, particularly at a college or university.
For example:
Dr. Gradgrind is our lecturer on the Victorian novel and the course will be taught through a series of lectures and seminars.
Please note: A seminar at a college or university is a class for a small group of students to discuss the subject with the lecturer.
instructor(n.) 教练、教员;(美)大学讲师
In British English, an instructor teaches you on how to learn or improve in a particular skill or sport.
for example:
If you want to learn how to drive, you will need a driving instructor.
If you want to learn how to fly, you will require a flying instructor.
Please note: In the US, an instructor is a university teacher below the rank of assistant professor.