ग
This letter is written as

This letter is pronounced as the sound of G in ‘Girl’ or ‘Goat’ in English. It is exactly same as English. It is represented as G in romanization as it is.
For Example:
गमला is read as GAMLA in Hindi which means Flower Pot or Vase in English. गदगद
गगन Gagan Sky
गरम Garam Hot
घ
It is written as follows:

This letter has aspirated sound of ग. While pronouncing ग there is no air released from mouth but while pronouncing घ some air is being released. This sound does not exist in English. In romanization it would be Gh.
Some examples in Hindi are
घर Ghar Home
घटक Ghataka Ingredients