Check online for free printable sign language alphabet charts. Type the phrase into a search engine to bring up a list of potential websites. Look through the highest hits but focus on websites belonging to nonprofit organizations such as PBS or universities. Other examples include those found at abcteach.com and apples4theteacher.com. Some websites might try to charge you. Ignore them because you have so many better options freely available on the Internet.
Visit your public library to see what kind of resources are available for someone trying to learn the basics of sign language. Alternatively, you can either call them to ask directly or check their website for information. Bigger libraries should carry sign language books while some might also run programs to help people learn sign language. You might be able to pick up some freebies from these programs. If not, you can also make photocopies of sign language charts found in books, provided that doing so does not violate copyright laws.
Use the Yellow Pages or a similar online directory to find a list of special needs schools in your local area. Although these schools are not obligated to provide you with the necessary resources unless you or your family member is a pupil at their school, the staff at such schools are often happy to help someone interested in learning sign language. Even if they can't provide you with the chart, they might be able to point you in the right direction.
You might also be able to find free sign language alphabet charts from other sources. Use a directory to find local chapters of organizations that promote the use of sign language such as the National Association of the Deaf. See whether you can get free alphabet charts from these organizations. If not, try asking local clinics and hospitals to see whether they offer free printable charts.