As with all the other languages, practice and constant usage goes a long way.

Tagalog does employ the principle of root words. I can't remember anymore the exact terms by which they are called but we have additions which you can put in front of a word, in the middle of the word, at the end of the word to change the use of a word or its meaning. The part where it can get overwhelming is when combinations of these are used so that you sometimes arrive with a very long word. There are grammar books available though to help you master this. This is taught to Filipinos starting at gradeschool. But to tell you the truth, even us Filipinos don't do well on Tagalog grammar tests. Conversational Tagalog is easier as you'll find it is simpler, you get clues from bits of English, Spanish words, and even words from other Asian languages that have become a normal part of our vocabulary.

To give you an example of the use of root words in tagalog.
WALIS - broom. (root word)
pagwaWALIS - act of sweeping
WALISan - sweep (command)
naWALIS - was swept away
and so on.

letters in the root word may also change.
BILI - buy
Bilihan - buy from / also can be "store" or place to buy from.
naMILI - bought
mamiMILI - buyer
namiMILI - buying

Here's probably the easiest language tutorial in Tagalog as it involves only one syllable "BA". Should you ever find yourself in an elevator somewhere in the Tagalog speaking regions, you can inquire if the cab is going down by saying "Bababa ba?" Pronounced BAHbaba (pause) ba (this last syllable has to be pronounced as if questioning... use a higher pitch than what you used with the first word.
If you get this answer "Bababa." (pronounced BAHbaba or just bababa in a rapid monotone), then that is a yes.... the elevator is on its way down.