The most important thing to know about rhyming slang, of course, is that most of the time it doesn't rhyme.
There are two reasons for this. Firstly, a lot of rhyming slang was invented in London in the early nineteenth century, and some of the rhymes only work if you have a nineteenth century London accent. For instance, a hot potato was a waiter, and round the houses was trousers.
(In the first example potato was (and sometimes still is) pronounced p'TAYter, and in the second trousers was TROWsiz.)
The other reason why rhyming slang doesn't rhyme is that the original very often consists of a pair of words, and the years have worn away the one that rhymes. For instance, apples and pears is rhyming sland for stairs; but I've never heard anyone say more than up the apples!
Sadly, I hear rhyming slang less and less, and when I do it's usually being used by fairly old people. Still, it's left its mark, and is used by all of us even if we don't realise it. For instance, the American brass tacks is rhyming slang for facts; and the Australian pom meaning immigrant could well be rhyming slang from pomegranate.
Thing To Do Today: blow a raspberry. This seems to be American, too. A raspberry, meaning a rude noise, has its origins in raspberry tart!