"Professor" is usually the title of a senior tenured position at a tertiary institution.
You can teach at college level without being a professor - and it is common for docs and post-docs to do some teaching.
To teach, you need to have a postgrad degree, experience teaching, and a good rep with the admin and other staff.
Personally you need people skills, a thick skin, and a love of the subject.
To advance, you need to do well academically to post-doc and beyond, do good research, get published (nobody cares how you did before doc which is a bonus). You will have noticed that professors are seldom picked for their teaching ability.