Panliligaw or ligawan are the Tagalog terms for courtship, which in some parts of the Tagalog-speaking regions is synonymous with pandidiga or digahan (from Spanish diga, 'to say, express').  Manliligaw is the one who courts a girl; nililigawan is the one who is being courted. 

In Philippine culture, courtship is far more subdued and indirect unlike in some Western societies.  A man who is interested in courting a woman has to be discreet and friendly at first, in order not to be seen as too presko or mayabang (aggressive or too presumptuous).  Friendly dates are often the starting point, often with a group of other friends.  Later, couples may go out on their own, but this is still to be done discreetly.  If the couple has decided to come out in the open about their romance, they will tell their family and friends as well. 

In the Philippines, if a  man wants to be taken seriously by a woman, he has to visit the latter's family and introduce himself formally to the parents of the girl.  It is rather inappropriate to court a woman and formalize the relationship without informing the parents of the girl.  It is always expected that the guy must show his face to the girl's family.  And if a guy wants to be acceptable to the girl's family, he has to give pasalubong (gifts) every time he drops by her family's house.   It is said that in the Philippines, courting a Filipina means courting her family as well.

In courting a Filipina, the metaphor often used is that of playing baseball.  The man is said to reach 'first base' if the girl accepts his proposal to go out on a date for the first time.  Thereafter, going out on several dates is like reaching the second and third bases.  A 'home-run' is one where the girl formally accepts the man's love, and they become magkasintahan (from sinta, love), a term for boyfriend-girlfriend. 

During the old times and in the rural areas of the Philippines, Filipino men would make harana (serenade) the women  at night and sing songs of love and affection.  This is basically a Spanish influence.  The man is usually accompanied by his close friends who provide moral support for the guy, apart from singing with him. 

Filipino women are expected to be pakipot (playing hard to get) because it is seen as an appropriate behavior in a courtship dance.   By being pakipot, the girl tells the man that he has to work hard to win her love.  It is also one way by which the Filipina will be able to measure the sincerity of her admirer.  Some courtships could last years before the woman accepts the man's love. 

A traditional dalagang Pilipina (Filipinpa maiden) is someone who is mahinhin (modest, shy, with good upbringing, well-mannered) and does not show her admirer that she is also in love with him immediately.  She is also not supposed to go out on a date with several men.  The opposite of mahinhin is malandi (flirt), which is taboo in Filipino culture as far as courtship is concerned.

After a long courtship, if the couple later decide to get married, there is the Filipino tradition of pamamanhikan (from panik, to go up the stairs of the house), where the man and his parents visit the woman's family and ask for her parents blessings to marry their daughter.  It is also an occasion for the parents of the woman to get to know the parents of the man.

During pamamanhikan, the man and his parents bring some pasalubong (gifts).  It is also at this time that the wedding date is formally set, and the couple become engaged to get married. 

Source:  http://www.seasite.niu.edu/Tagalog/love.htm