How can I build a kitchen island?

kitchen cabinets screwed together for a base, then a countertop to fit. be careful what you wish for. do a mock up with cardboard boxes before you purchase materials. live with it for a month. see if its a pia or useful.

I've seen people use an old dresser that is a bit taller and add wheels to it.

I am using my mom's old microwave cart since I have a small narrow kitchen and it works wonderfully. It has a nice wood top that we keep lemon oiled, but I have a large cutting board that I keep on top of it anyway so that it stays nice. I didn't have to paint or restain it, so it worked out great. Check out Restore stores and Salvation Army stores, you never know what you will find that will suit the look you want. If need be, put good metal plate castors made for the weight of the weight of the island.

https://www.hometalk.com/diy/bedroom/dressers/repurposed-dresser-into-custom-kitchen-island-6371832