There's nothing difficult about using these words. You can say 'I saw an advert for that shampoo in a magazine' or 'I put an advert in the local newspaper' or 'There are too many adverts on TV these days.' There's no difference in meaning between them. 'Advert' is simply a short form of 'advertisement'. 'Ad' is an even shorter one. These words are different from 'advertising', though. 'Advertising' is a more general noun, and it is uncountable. 'Advertising' is an activity connected with marketing. For example, someone who creates adverts would say 'I work in advertising.'

Advert and advertisement are synonyms of eachother in their noun forms, but in their verb forms they are not for advery is to remark or comment; 1)He adverted briefly to the news of the day. or to turn the attention; 2)The committee adverted to the business at hand.

"Advert" is very rarely heard in the US, if at all. We say "ad" or "advertisement".

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