Have you read any privacy notices recently? Generally, they bamboozle people with legal language and wording. Under the GDPR this is no longer aloud.
Personally, I love that the GDPR is stating that we have to communicate in plain language that our audiences can understand. So while your privacy notice still has to be legally correct, and you absolutely get your legal team to sign off, your privacy documentation should be written with your audience in mind. For example, if your website is aimed at anyone other than legal folk, get a non-legal person to write the notice.
In particular, if you target children and you need parental consent you need to make a reasonable effort that it’s actually the parent who consented.
There is no one better in an organisation to write your privacy notice than marketing. We know our audiences best and speak their language. You may even decide that your audience is very visual and create images or video to explain your privacy.
The best tip we can give you, write your notice, get legal to sign off and then check with one of your customers whether they can understand it. If not, it’s back to the drawing board.