How can I buy an Apple phone watch?

No such thing as an "Apple phone watch". Its just called Apple Watch.

If by "Phone watch" you mean a Cellular / Mobile capable Apple Watch, select the GPS+Cellular models of any Apple Watch you want to buy.

Use a cellular network

Apple Watch GPS + Cellular models can connect to cellular. With a cellular connection, you can make calls and use data or apps when you don’t have your iPhone or Wi-Fi. Learn how to add your Apple Watch to your cellular plan.

Do note, you will still need an iPhone to set up and use the Apple Watch.

Start at this web page: Apple Watch - Compare Models - Apple

When you find one you like, click buy and then proceed.