You can use the Insert Button option within Google Sites to create buttons on your website. Once you add your button, you will be given a few edit options but not many. See some additional options below.
You can create buttons on websites like Da Button Factory, but I prefer to create my own buttons using Google Slides because it gives me more flexibility. You can make a copy of my template below to create your own.
Once you add your button to your website, you want to select your button and add a link to it.
Choose URL option if linking to an external website
Choose Page if linking to a page within your website