By destroying it, replacing it, enhancing it--the full range of how anything is changed. Seriously. This question is too big to be answered here. There are probably thousands of books on cross-cultural impacts. I'll list just a few of the changes that can be observed today (and why are third world countries the focus of the question?). Any culture is impacted when two cultures come in (close) contact:
KFC chicken Uncle Wu's Chicken (China)
McDonald's Chinese Golden Arches (everywhere in China)
International Branches
Fashion Mini-skirts under chadors (Iran)
Universal diving licenses Arabian women (secretly) driving
The Use of Fossil Fuels Nigerian poverty, Kuwaiti wealth
Mobile Phones African farmers connected to the market
Improved Medical Practices UN World Health Organization aid
Improved Medicines The elimination/reduction of world diseases
Starbucks Coffee International Branches
The use of English loanwords Corruption/elimination of other languages
Japanese, Farsi, French, etc.
Cuisine International cusine (Indian curries, sushi.)
Transportation From camel, donkey, horses to cars, buses,
trains, aeroplanes et al.
This is obviously not a comprehensive list and it does not make clear another interpretation of the question "how". This could be answered by saying by means of television, education/textbooks, internet research, travel, even person to person contact/discussion.
I have always wondered why this idea of "third world countries" and "a third world culture" have become thought of as a homogenious intercontenential culture? When in-fact there are many cultures, diverse peoples, ideas, and landscapes.
Secondly from those who have used that term in my presence there is a sense of romanticism,
As far as I can tell the term "third world" has two originans, one economic and one derogatory. So whenever I hear the term I always wonder in which context is the word used in.
Last, the word interculturalism. This word to I have the same questions as to the context the speaker is using it in. It appears to me that an idea of culture having not already been affected by other cultures, intermingling, and modernization is a naive. Could it be a hope by some that we have not exported the inhuman way we act toward ourselves and others as "first and second worlds"?
To answer the question directly, death and exploitation.