pau-kurt10, welcome to Australia, Adelaide eh!
Adelaide is in a gulf that is quite deep and doesn't get a lot of surf but as you go south along the coast from Glenelg eventually to end up at Victor Harbour and Goolwa Middleton ( also known as Dribbleton) there are quite a few spots at a good learners level.
At some of them a surf school operates.
I especially advise you not to surf alone because some of the areas are dangerous in themselves and some are noted for being places where great white sharks hunt.
This surf school might be your best bet as they have all the equipment and can teach you about beach sense and other things you need to know.http://www.sasurfschools.com.au/sa-surf-schools.php
There are very good spots further west from Adelaide on the Yorke and Eyre peninsulas but they are more for skilled surfers and are a serious expedition and even more sharky.
I've taken up troll hunting just for fun, instead of a rifle I'll just use a pun!