There is no requirement for legacy to become a Freemason.
If you would like to get information regarding your Grandfather or Mother's masonic history, contact the Grand Lodge and Grand Chapter (respectively) in the jurisdictions (in the USA this is by state) they were active in. They can help you with the lodge and chapter records, affiliations, etc.
If you want to become a Freemason, contact your local lodge, introduce yourself, and tell them you are interested in joining - they will take it from there.
Requirements to be a Freemason:
1) Belief in a Supreme Being (you may refer to Diety as God, Allah, Jehovah, whatever - your faith isn't judged, you just need to believe in a Being greater than yourself)
2) Be of lawful age (18-21, depends on jurisdiction)
3) Be of good moral caliber
Once you fill out a petition to join a lodge, you submit your initiation fee (should be refunded if you're not accepted - ask the secretary). It will be reviewed in Lodge and investigated. You will get a chance to meet with an investigative committee - ask all the questions you like at any time - they will be very frank. Once it's investigated, it will be brought up for a vote - if elected, you will be initiated and start your own masonic journey.
If you need help finding a local lodge, Grand Lodge or Grand Chapter for your research, or if you have any other questions, contact me through my YA profile and I'll help where I can.
I recommend reading this - it's from my Grand Lodge (North Carolina) and the information is generally applicable to any jurisdiction:
http://www.grandlodge-nc.org/freemasonryrevealed/index.htm