Here in the US, an assistant professor is an entry-level tenure track appointment but does not come with tenure. An associate professor is the next level up and does come with tenure. Tenure track appointments virtually always require a PhD but not necessarily from a US institution.
A lecturer appointment is a teaching position, almost never comes with tenure, and does not necessarily require PhD, though it does usually require a master's at minimum.
A typical initial contract is three years.
Open positions are often but not always posted on the department website. Contact the department you're interested in for more info. Typically, you'll be asked to supply a CV, references, various statements describing your objectives, teaching philosophy and research interests, and possibly a teaching demonstration video. Obviously, all of this depends on the department.