Which is the correct way to say?
I am going to take a shower.
I am going to take shower.
We always use the indefinite article. In BrE we usually say "have a shower" and "have a bath", in AmE it's "take a shower" and "take a bath".
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.
Not a teacher!
You might also want to look up 'take': take - Definition and pronunciation | Oxford Advanced Learners Dictionary at OxfordLearnersDictionaries.com
There are also expressions with 'take' where you do not use any article, e.g. 'take sugar', 'take control' or 'take cover'.
Then there are expressions with 'take' where you use the definite article, e.g. 'take the blame' or 'take the mickey' (an example of which follows below).
When it comes to cleaning one's body in a shower or bath I prefer the BrE way to express these activities. If somebody were to ask me, 'Have you taken a bath?' my reply would be, 'Why, is one missing?'
When you read through all the entries for 'take' you will see that this is a very important word. I only hope you won't shout after you have finished reading, 'I can't take it anymore!'