I recently came across a talk on LDS.org which was given when I was in grade school (about 9 years before I even stepped foot inside an LDS church), but is still just as applicable today. I had never considered the difference between searching and seeking, but Elder Russell explains it well:
"The Lord requires us— yes, you and me— to locate the less-active members and help them to return to the fold.“For thus saith the Lord God; Behold, I, even I, will both search my sheep, and seek them out” (Ezek. 34:11). Yes, we are to both “search my sheep” (locate them) and then “seek out” (bring back) less-active members and families, with unending and unqualified love. And in the process, we and they shall learn the true meaning of “ye shall … find me, when ye shall search for me” (Jer. 29:13).
Elder Russell also describes the process by which less-active families can be approached and encouraged to return to activity:
#1- (The servants of the Lord fast and pray)...that the Lord (will) indicate to them the choice families to be visited
#2- The chosen families (are) then (contacted and arrangements are made) for visits.
#3- "The servants of the Lord...visit the less-active families"
#4- (The servants of the Lord) assure them of the redeeming love of the Lord and their love for them. They speak not only by inspiration, but by a higher law, in which the Spirit of the Lord speaks through them. Through constant prayer in the heart, what is said is by the Spirit of the Lord.
#5- The family remembers that the Lord truly loves them and (recognizes) that the servants of the Lord love them as well.
#6- Then the Lord returns the family to the fold.
"Touching the Hearts of Less-Active Members," Elder Gardner H. Russell of the First Quorum of the Seventy (November 1986 Ensign)