Getting around in Albion Online is very time consuming. Because of this, owning a horse is considered one of the first objectives of every player.
A few styles of horse are available to those who buy the Founder’s Packs. Otherwise, the easiest horse to unlock is available through the starter questline. You’ll have to finish quite a few quests to get to the point where you are given a horse, but you’ll get there eventually.
Once you have a horse, you need to equip it in your inventory. Then, simply press ‘A’ on the keyboard to jump on the horse and gallop around.