Hi, does anyone know how to upgrade a Stable?

The easiest way is to buy the stable blueprint one level above your current stable (you can find your stable's current level under Manor -> Buildings). If you have a lvl 1 stable, you'd get yourself a Blueprint: Stable (lvl 2). You'd then use the blueprint in your warehouse so that it appears in your Craft & Construction tab. Then it's just to collect the materials and the pet to fulfil the requirements and craft your new stable. If you want to take a look at what materials each upgrade requires, you can find that here: https://beastkeeper.com/recipes-list.

The alternative is an Expand Stable Scroll, which gives you 10 extra slots, but that's a much-desired Premium Store item so it'll be more expensive.