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 you need follow next steps:
1. Copy layout file
from: app\design\frontend\base\default\layout\newsletterpopup.xml
to: app\design\frontend\YOUR\THEME\layout\newsletterpopup.xml
2. Copy html files
from: app\design\frontend\base\default\template\newsletterpopup\
to: app\design\frontend\YOUR\THEME\template\newsletterpopup\
3. Copy css file
from: \skin\frontend\base\default\css\newsletterpopup.css
to: \skin\frontend\YOUR\THEME\css\newsletterpopup.css
4. Copy javascript file
from: \skin\frontend\base\default\js\newsletterpopup\newsletterpopup.js
to: \skin\frontend\YOUR\THEME\js\newsletterpopup\newsletterpopup.js
5. Copy images directory
from: \skin\frontend\base\default\images\newsletterpopup\
to: \skin\frontend\YOUR\THEME\images\newsletterpopup\