Extension package is build according to Magento guidelines. Installation process is usual. Please follow How to Install an Extension in Magento 1 article.
Custom theme
If you are using custom theme, then you need follow next steps:
Copy layout file
from: app\design\frontend\base\default\layout\mt\giftcard.xml
to: app\design\frontend\YOUR\THEME\layout\mt\giftcard.xml
Copy html files
from:from: app\design\frontend\base\default\template\mt\giftcard\
to: app\design\frontend\YOUR\THEME\template\mt\giftcard\
Copy css files
from:from: \skin\frontend\base\default\css\mt\giftcard
to: \skin\frontend\YOUR\THEME\css\mt\giftcard
Copy javascript file
from: \skin\frontend\base\default\js\mt\giftcard
to: \skin\frontend\YOUR\THEME\js\mt\giftcard