You can craft mounts using the Crafting menu that can be opened from the Menu Bar. Every race has their own racial mount they can craft which requires one Steedgrass. You can get steedgrass by performing one of your first starter tasks (press the J key), killing select monsters and/or by gathering from bushes with a sickle.
Once you craft a mount it will spawn a figurine in your backpack. Be careful as these can weigh a lot and can greatly slow you down if you have too many in your inventory.