Colons are used for a variety of purposes.
The most well known is to introduce a list. 'For this recipe you will need:' and so on.
Colons are used to introduce quotes and sometimes direct speech.
Or between two main clauses where the latter explains or adds further to the first. A main clause includes a subject 'Yorkie' and a verb 'watched'. Yorkie watched the trains: the rain poured from the sky.
Apostrophes are used to indicate possession and to indicate omission, I.e. Missing letters.
In didn't - we have shortened the word from did not. We use the apostrophe to indicate the missing letter o. It's the same in they're (they are) and it's (it is).
The more confusing part is possession. If we want to indicate possession of something, Mr Hudson's laptop, we generally add the apostrophe between the noun and the s. Unfortunately things can get a bit more confusing when looking at plurality or words that end in s. The fairies' mushroom, the class' pens etc.
This is darkened even further when newspapers and magazines use 's after common nouns and just an apostrophe without the s after a proper noun.
Generally if you can say the sentence without hearing the extra s you can add the apostrophe afterwards. I.e. Sarah Jones' room. When we say class as in my example above, we find ourself saying 'classes' so some add the apostrophe s after the final s - class's.
Very confusing!