You need to setup the domain in Route53 first (eg example.com), as part of the setup you get 4 name server addresses. You change the name servers at GoDaddy to your AWS nameservers as their support describe, which authorises Route53 to host your DNS. From then on you manage your DNS from Route53, not GoDaddy (but GoDaddy are still your registrar).
Once your nameservers point to route53 follow the docs on creating an alias in route53
If you want to use your own domain name, use Amazon Route 53 to create
an alias record that points to your CloudFront distribution. An alias
record is a Route 53 extension to DNS. It's similar to a CNAME record,
but you can create an alias record both for the root domain, such as
example.com, and for subdomains, such as www.example.com.
When you change the nameservers on GoDaddy any DNS you setup there will no longer be visible on the internet, only whats in Route53. Transfer any records you have created in GoDaddy to Route53 before changing your nameservers. Ignore any DNS records you didnt create.
If theres a problem you can goto GoDaddy and reset the nameservers back to default and that will restore the previous DNS.
One thing to mention - TTL - time to live. If DNS records have a high TTL (in seconds) it means when you make changes it will take upto that amount of time for everyone to get the update. The TTL will be visible in GoDaddy, or you can search "DNS dig" to find online tools that read DNS. The TTL of the NS records might be high (days, a week etc) - this will effect how long it takes Route53 to fully take over responsibility of your DNS.