The Markers NG and NI/NINA

A.   NG

The marker NG covers a broad range of meanings, and there is no one exact translation of NG in English. In the most general sense, NG indicates that there is some type of relationship between the word that follows NG and another words in the sentence. The exact meaning of NG depends on the situation or context of the sentence.
There is one important thing to note about NG: this marker indicates that the word that follows it is not the focus of the sentence. In that sense it is the opposite of the marker ANG. It's like NG is the "evil twin" of ANG. Or if you like Star Trek,  you can think of ANG as "matter" and NG as "anti-matter."  If I see a NG in front of a word, then I know that word isnot in focus. But if I switch the marker NG to an ANG, suddenly the word is in focus. Let's practice:

Ng house (the house is not in focus)

SWITCH!

Ang house (the house is in focus)

Functions of marker NG in Tagalog sentences
The marker NG has three major functions in Tagalog. They are outlined in this section.
1. NG indicates possession. The possessor noun marked by NG comes after the noun
    possessed. In other words, the word that comes before NG is the thing that is possessed
    or owned. The word that follows NG is the possessor or owner. Here are some examples:

bahay ng pamilya Santos	house of the Santos family
kotse ng babae	car of the woman
ang titser ng mga bata	the teacher of the kids
ang hardin ng matandang lalaki	the garden of the old man

2. NG marks the direct object of a sentence if the direct object is not the focus.
What is a direct object? A direct object  is the receiver the action (of the verb). Let's look at a sentence in English:

John hit the wall.

In this sentence wall is the direct object. It received the action of the verb. The wall was the thing that was hit.
In Tagalog, NG is used to mark the direct object (when the direct object is not focused).  However, if the direct object is the focus of the sentence,  then ANG would mark the direct object.  Below are some examples:

Bumili si Ana ng lapis sa tindahan.	Ana bought a pencil at the store.
Nanood sina Pedro ng sine kahapon.	Pedro and friends watched a movie     yesterday.
Nagbasa ako ng libro sa laybrari.	I read a book in the library.
Naglinis kami ng bahay noong Linggo.	We cleaned a house last Sunday.

3. NG marks the unfocused doer (actor) of the action of the verb.
Let's look at the sentence we used before:

John hit the wall.

In this sentence John is the actor or doer of the action. If the actor is not in focus, then NG marks the actor. If the actor is in focus, then ANG (or SI) marks the actor.  Below are some examples of NG marking the doer of action:

Ibinigay ng titser(Actor) ang libro sa    estudyante.	The book was given to the student by the    teacher(Actor).
Binigyan ng titser(Actor) ng libro(Direct Object) ang    estudyante.	The student was given a book(Direct Object) by the     teacher(Actor).
Sinulat ng makata(A) ang tula para sa    nanay.	The poem was written by the poet(A) for      mother.
Sinulatan ng makata(A) ng tula(D.O.)     ang nanay.	Mother was written a poem(D.O.) by the     poet(A).

Notice that in some of the above sentences there is more than one word marked by NG. Let's take a look at the second sentence:

Binigyan ng titser (Actor) ng libro (Direct Object) ang estudyante.

Notice that both titser  (the actor) and libro  (the direct object) have NG in front of them. The focus of the sentence is estudyante  (it has ANG in front of it).  Because titser is not the focus---it has NG in front of it--and because libro is not the focus---it too has NG in front---we can see that NG can mark both the doer of the action and the object that recieves the action.

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B.  NI and NINA
The markers NI and NINA mark personal names (e.g., Bob, Jill, etc.) that are not the focus of the sentence.
You remember how ANG marks the words that are in focus except for names of people? When personal names are in focus, they are marked by SI. In the same way, NG marks the words that are not in focus except for personal names. When personal names are not in focus, they are marked by NI and NINA.
Just as with ANG and NG,  you can think of NI as being the opposite of SI. It's like NI is the "evil twin"  of SI.  If I have a NI in front of Bob, then Bob is not the focus. But if I "flick the switch" and change NI to SI, then (click) I have suddenly made Bob the focus of the sentence. 
Functions of markers NI and NINA
NI marks the name of one person, and NINA marks the name of two or more people. These markers basically  have some of the functions of the marker NG.
1. NI and NINA indicate possession. The possessor noun comes after the noun possessed.
    Or in other words, the noun before NI is the noun that is possessed or owned. The noun
    after NI is the possessor or owner.  Below  are some examples:

kaibigan ni Juan	a friend of Juan
kaklase ni Maria	a friend of Maria
ang bahay nina Tina	the house of Tina and family
ang libro nina Fe at Kim	the books of Fe and Kim

2. NI and NINA mark the unfocussed actor/agent (when the actor/agent is a personal name). Below  are some examples:

Binili ni Rita ang damit sa tindahan.	The dress was bought by Rita at the store.
Binigyan ni Jose ng pera si Bob.	Bob was given some money by Jose.
Niluto nina Tony ang isda sa kusina.	The fish was cooked by Tony and company     in  the kitchen.
Itinapon nina Fred at Melvin ang  basura    sa labas.	The garbage was thrown outside by Fred     and Melvin.