About the word Kiru...

How do you properly speak the word Kiru(Wear) and Kiru(Cut)? And how do you tell the difference? As a matter a fact, how are you able to tell the difference to other certain Japanese words that sounds exactly alike?

Of course, the context is enough to tell the difference most of the time, but not all the time.
And yes, there is a difference in pronunciation between apparent homophones like kiru "to cut" and kiru "to wear" : the difference is in accent. Japanese has a pitch accent (different from English accent which is a stress accent) : there is a difference of height ("tone") between the syllables of a word.
For example kiru "to cut" is pronounced with a high-low melody (HL, fall of the pitch after the first syllable, between ki- and -ru) while kiru "to wear" is pronounced low-high (LH).
For each word in Japanese, the accent pattern is fixed. What matters is whether there is a pitch fall or not, and if yes where. Some dictionnaries and textbooks give the accent patterns : the so-called unaccented words have no pitch fall and a LH(...H) pattern (first syllable low, all the following high), others have a basic pattern of (L)H(...L) (first syllable low, all following high until the pitch fall, and then all low, or first syllable high if immediately followed by a pitch fall)