When you recognize Jesus Christ as the Lord and believe in your heart that He died on the cross to save us from our sins, you're saved. The penalty for sin is infinite and eternal. Only God could pay the penalty for us. Since God could not die, He paid the penalty with His perfect one and only Son, Jesus Christ, and whoever believes in Him will not perish but have eternal life (John 3:16). Salvation is a free gift that God has given to all of us. It has been done and can never be taken away from us. All we need to do is to accept and profess that Jesus Christ is the risen Lord. 
It's important to keep in mind that our faith in the Lord Jesus Christ will not automatically save our family. Salvation is a personal experience, and no one can accept it on anyone's behalf. We can, however, make conscious efforts to make sure our family members see God's glory through us so that they will believe and be saved!

Dear Heavenly Father, You have overcome death and given us a new life, a life with Your eternal love. I pray You help me share Your everlasting love with my family and all the people around me so that they may accept You as their personal Savior and enjoy Your salvation as well. Thank You for Your unconditional love and salvation! 
In Jesus's name I pray. Amen.