You need to set up your Apple ID.
See this support page to get that done.
Your Apple ID is easiest to use if you have payment information like your credit card entered. If you want to download a free app you will be asked for your password but you will not be charged anything for a free app.
You will be charged for apps that have a fee.
There is a way to set up an Apple ID without entering payment information. Read carefully through the support pages to find that info. As I said previously though, it is more convenient to have payment information stored in your Apple ID account.