Involving parents in the process of assessment isn't a difficult thing to do. Doing it well is difficult.
One strategy that promotes parental involvement in the assessment of students is to use a grade book that publishes grades to a "parent portal" that gives a parent the ability to view their child's grades. Ideally, this parent portal alerts parents of upcoming tests and projects; however, it is an effective tool at simply conveying student scores to parents. Additionally, parents can typically see if various assignments are missing. The downside to this particular strategy is that it is reactive. Parents see the results and don't have any control over the assessment that previously happened. Additionally, it is fairly impersonal.
Parent-teacher conferences can be another strategy that promotes parental involvement in student assessment. These conferences fix the impersonal problem, and they attempt to address some of the reactive nature of the online grades. The conferences allow a back-and-forth discussion to occur between parent and teacher, and the conversation tends to focus on student achievement and how the student is performing on a day-to-day basis.
Another face-to-face strategy is to have a back-to-school night. This event has parents on campus, and they get to meet each teacher. Teachers spend time introducing themselves, going over the course content, and explaining the various assessments that will happen over the course of the year.
Finally, a teacher can attempt to have the parents be involved in the actual assessing of students. This can be tough to do, and certain subjects lend themselves more toward this kind of implementation. A speech and debate class might invite three to four parents into the classroom to be the judges of the competition. This is a great strategy to involve parents in the assessment process; however, it is very limited in the number of parents that can be involved.