After beating "Burning Desire", Denise (Available -) will become your first girlfriend automatically.
You'll have the opportunity to meet Michelle Cannes (- & -) at driving school in San Fierro, Helena Wankstein (- & -) in Blueberry on the Ammu-Nation range balcony, Barbara Schternvart (-) in the police parking lot in El Quebrados, and Katie Zhan (-) in Avispa Country Club in San Fierro.
Once you have enough respect, walk up to them and hold R1 to target them.
Now press up on the D-Pad and they will be recruited.
Millie Perkins (- & -) will automatically become your girlfriend after you complete "Key to Her Heart".