You won't have your Diablo 4 mount right from the start of the game. Instead, you'll need to work your way through the campaign and complete Act 3 of the story to access it. Any additional mounts you've acquired, either through Twitch drops or as a preorder bonus, won't be available to use until you've completed the quest to unlock mounts either. Thankfully, this only applies on your first time through, as mounts will automatically unlock at level one with subsequent characters.
The world of Sanctuary is large, but at least you won't be tempted to dash past enemies that can give you valuable XP. You'll have to spend the first 30 levels running around on foot, but the good news is that you can fast travel around the world using waypoints when running just gets too strenuous. That said, if you want to learn exactly how to get your mount in Diablo 4, here's how to unlock it.
How to get your Diablo 4 mount
After you've finished Act 3 of the campaign, you're sent to Kyovashad to speak with Donan in the Cathedral of Light. If you stick with the campaign and don't do any side quests, you will likely reach this point at around level 30. Once you speak with Donan, you'll receive the Mount: Donan's Favor quest.
It's fairly straightforward from this point: head to the southwest of Kyovashad's waypoint to find Oskar the Stable Master and speak to him. You'll get your first mount for free, though you can buy two others from the vendor section of any stable master's menu for 20,000 gold each. You can also customise your mount with trophies and barding here.
To use your newly acquired mount, simply call it with the Z key, and get a burst of speed with your evade key while riding. One thing to be aware of is that your mount will get scared and spooked if they're around too many enemies—if the bar above the horse UI head fills completely, you'll be knocked off.
Each class also gets their own "mount skill", which you can use to dismount quickly and jump straight into a fight. The sorcerer skill, for example, throws a wave of ice at the spot where you dismount, briefly freezing enemies and allowing you to get a few hits in before they can respond.
How to get new mounts and cosmetics
There are lots of other mounts and accessories that you can find across Sanctuary, including the Spectral Charger; a ghost horse that randomly drops from the Gathering Legion world event at Kor Dragan. While most mounts and cosmetics simply have a chance to drop as monster loot, or from chests in each region, you can also buy them for Red Dust from the Unconventional Steed Armor Vendors found in the PvP Field of Hatred zones.
Certain cosmetics also have a chance to drop when you complete specific activities or defeat bosses. Each of the three world bosses, for instance, can drop a mount cosmetic when you beat them, as can The Butcher. Lastly, you can buy mount cosmetics for real money, but I'm not sure why you would when there are plenty of great free ones you can get.