Meaning of “umakyat ng ligaw” -
The short answer:
It means, “to court (someone) romantically”. It is often used intransitively.
“Pwede ba akong umakyat ng ligaw sa bahay ninyo mamayang gabi?” = May I court you at your house tonight?
The long answer: :-)
The typical Filipino house in the olden days has 2 floors. The residents live on the second floor, while the lower floor is normally used for storage or even as a stable. Moral standards then also dictate that the proper place for a guy to court a girl is at her house. (The upside of that is it saves the guy the trouble of having to worry about meeting his possible in-laws still at a future time. :-) ) The guy, therefore, has to go up to the second level of the house to see the girl. That’s where the use of “akyat” (climb, go up) comes from.
The meaning of “ligaw” would depend on which syllable you put the stress on. If the stress is on “li”, then the meaning is “courtship”; if it’s on “gaw”, then the meaning would be “to lose one’s direction” or “to go astray”, as in “stray bullet” (ligaw na bala) or as si_kano has mentioned, “wild” as in “wildflower” (ligaw na bulaklak).
Originally, “umakyat ng ligaw” literally meant “courtship by going up the stairs”. However, nowadays the architectural and moral norms have already changed such that “akyat” is no longer a part of the courtship process. A few people now may still say “umakyat ng ligaw”, but it would only be in the figurative sense.
We normally just use "ligaw" these days in these forms: (the numbers indicate the syllables where you put the stress)
Lumigaw (2; subject-focused: infinitive, imperative, and past tense); lumiligaw (3; present); liligaw (2; future).
Ligawan (2; object-focused: infinitive and imperative); niligawan (3; past); nililigawan (4; present); liligawan (3; future) – notice that in this form, the accent is on “gaw”.