I have no way to upgrade my stables. How do you upgrade the stables? Thanks!

First you need to find the Blueprint: Stable (level 2). You can either find this while exploring islands (it is random what you get though, so it may take you a long time to find), you can buy it from the State Store (for an outrageous amount of money) or you can get it from other playersn through the Item Auctions or Trades. Alternatively you could look around on the Forum - there are often people who give away blueprints and schemes they have no use for anymore.

Anyway, once you have the Blueprint, go to your inventory, find it, click it and select "Use". You will then learn how to build your upgraded stable. 

Next, go to Manor -> Crafts & Construction and find the stable. If you have all the materials and a pet that is good enough to build it, you can select the pet from the dropdown menu and instantly start building. Four hours later, you will have your new stable. If you do NOT have all the things required, you can click on the stable to see what you are missing. 

This is the exact same way of how to make all the other available buildings too by the way.