Undecided questions
When to use ‘di’ in Italian;

I would be grateful if someone could help with when to use ‘di’ in Italian sentences.

The only ‘rule’ that I know is;

‘a noun followed by a verb in the infinitive requires di’

and that you;

‘often use ‘di’ after many verbs of communication’

So I’m assuming that after ‘to tell’, ‘to say’, ‘to ask’, ‘to hear’, ‘to shout’, ‘to telephone’, to argue etc ‘di’ is used.

However, very often, verbs or adjectives are followed by ‘di’ but in other cases are not, for example;

Spero di partire (Speriamo = verb + di)

Penso di partire (pensare = verb + di)

(Not sure if the above examples ‘speriamo’ and ‘pensare’ could be classed as verbs of communication??? If not then don’t know why ‘di’ is used here?)

Abbiamo finoto di farlo (finare = verb + di)

Sono molto felice di vederla (felice = adjective + di)

But;

Mi fa molto piacere vederla (piacere = verb but no di??)

Desidero stare qui (Stare = verb but no di??)

I cannot find any rule that would explain why ‘di’ is used after some verbs/adjectives and not after others?

My Italian is still at a (very!) basic level and I would very much appreciate someone explaining this to me.

Kayleigh