There are many different ways to compile portfolios that reflect a child's home education progress. New Hampshire statute requires portfolios include a list of books the child read (it doesn't have to be comprehensive) plus a sampling of work in each subject from different points throughout the year. The reading list can be very simple; it can be just a list of title, including any you read to your child. It does not need to include page count or minutes spent. The work sample should be from different points in the academic year -- beginning, middle, and end. It must be kept for two years. This process can be very helpful later if your student enters a public or private school, or to prepare a transcript for college applications.
Some families like using a scrapbook approach with photos and mementos that reflect the student's activities and accomplishments. Some families keep the entire portfolio in an electronic form, including photos, videos, and scanned documents. Some maintain a blog or other online presence that documents the year. Other families just throw everything into a box. It's all good! There is no one right or wrong way to approach it.
In addition to including a variety of work samples such as tests, quizzes, and worksheets, be sure to also document writing projects, fine arts works (photos or recordings), science projects and labs, details of extracurricular activities, volunteer or career related work records, grades and work samples from any public school or online class providers, and field trips.
For those interested, below are resources and portfolio service providers.