how do i update my macbook which uses safari to the latest version

Check the computer requirements shown in each link to see if your computer is capable of running that OS version.

macOS Big Sur is compatible with these computers

Catalina

How to upgrade to macOS Mojave - Apple Support

How to get macOS High Sierra   

Sierra download

You can try to download it at the link below. If it won't let you, then your only options are to upgrade to Sierra/High Sierra/Mojave or find an older computer where you can download it using your Apple ID.

El Capitan

Check to make sure your applications are compatible. PowerPC applications are no longer supported after 10.6.       

Application Compatibility

El Capitan 10.11 Compatibility information 

macOS Sierra 10.12: Compatible Apps

Also check to make sure there is a compatible driver for your printer.

Do a backup before installing, preferable 2 backups on 2 different drives.

I believe that you are looking to upgrade your operating system. An upgrade installs a newer OS, such as changing from Catalina to Big Sur. An update installs a newer version of the same OS. An upgrade will often install a newer version of Safari, since it is part of the OS. Upgrades are found in the Apple App store. However, what you can upgrade to depends on the year and model of your Mac and you have not told us what that is, so we can not advise you what can be installed.