Tone sandhi

Tone sandhi ("sandhi" is from the Sanskrit word for "joining") is the change of tone when certain tones are pronounced successively.

In Taiwanese, most syllables will have to change tone depending on the surrounding words and grammatical function. The rules for this are extensive. Basically, it's a way to join syllables into words as well as to join larger units.
Almost all verbs and adjectives will change tone to "join" them to whatever is coming next in the sentence, if present.
The final syllable in a noun doesn't change tone, as long as it's standing alone. (If it's being used as an adjective, see above.)

Basic rules (Tone Circles)

Taiwanese tones in isolation, and the changes they undergo when they precede another tone.

If the original tone number is 5 (curving-up tone), pronounce it as tone number 7 (basic).
If the original tone number is 7 (basic tone), pronounce it as tone number 3 (low-falling).
If the original tone number is 3 (low-falling), pronounce it as tone number 2 (shouting out).
If the original tone number is 2 (shouting tone), pronounce it as tone number 1 (high).
If the original tone number is 1 (high tone), pronounce it as tone number 7 (basic).

If the original tone number is 8 (high-short), pronounce it as tone number 4 (low-short).
If the original tone number is 4 (low-short), pronounce it as tone number 8 (high-short).

We admit this is a simplification. Please see Taiwanese Hokkien#Tone sandhi for a more detailed explanation.

more detailed rules have been posted at Wikipedia: Taiwanese Hokkien#Tone sandhi, esp. special cases involving suffix ar (仔) and triplication
syllables ending in "h" are usually pronounced in shouting tone, such as in bahzaxng, but not bøeq
khix ("to go") is usually treated as if originally "khiq"