Being
For basic "is being" sentences, you simply add the Action/Actor conjugation to an adjective.
"She was being quiet." — "Naghipos siya." (hipos = quiet)
"The cat is being annoying." — "Nagasabad ang koring." (sabad = annoying, koring = cat)
"The car will be quick/go fast." — "Magdasig ang salakyan." (dasig = fast, salakyan = vehicle)
For general statements, like "Ron is rude," (in general, as opposed to "Ron is being rude" at a specific time) you can use regular description sentences (Descriptions Lesson). Emotions are also treated differently (Emotions Lesson).
Becoming
The word for "become" is "pangin," but you will rarely hear that word in that form. It is often contracted from "nagpangin" to "nangin," and from "manpangin" to "mangin."
"The duck became white." — "Nangin putî ang pato." (putî = white, pato = duck)
"You will become powerful." — "Mangin gamhanan kamo." (powerful = gamhanan)
Present tense for the word "pangin" is a bit different. You can use "nagapangin," which matches with the English "is becoming." However, it doesn't seem to used very commonly. This may be because a change that is ongoing (present tense) won't be completed until later (future tense), so "mangin" can also be used in this case.
Overlapping Usage
While there is technically some separation between "being" and "becoming," the overlap is substantial. For example, consider this sentence: "The child was feeling better." In this case, the child was "being" healthier, but the child also "became" healthier. As a result, the two different approaches have sort of merged.
In modern times, the "being" approach (nag, naga, mag) is quite commonly used in both cases. In older writing you can see the "becoming" approach (nangin, mangin) used in both cases. "Nangin" and "mangin" are still used today, but they seem slightly more formal.