Any guild member can go and catch a Baby Elephant. You will need to buy Peanuts from a Stable Keeper (most stable keepers in Valencia should sell them) or Guild Stable Manager. These will cost 50,000 silver each and I would recommend buying at least 3. You will also need to buy capturing ropes from a Stable Keeper. Depending on how much experience you’ve had with catching horses, buy between 3 – 10 ropes.
Elephants spawn in locations shown below (click image to enlarge):

Once you have found an elephant you can begin to capture one. Be careful of nearby mother elephants because they will come to attack you when you throw the rope. It is safer to kill the larger elephants before attempting to capture the baby, they don’t do a lot of damage, but have a lot of knockdowns which can be annoying.
When you are ready, right-click the capturing rope to use it. Aim the rope and left-click to throw it. A bar will show up on the right and you need to press the space bar and land it in the red area of the bar. You cannot let the bar go up and down, you only have one chance to land it in the area. If you miss the area or don’t press the space bar you will lose the capturing rope.
If you manage to get the rope over the elephants head you will now be able to start moving towards the elephant using W, A, S and D. If you see the elephant start to pull away from you, press the space bar to start the mini-game. If you do not press space bar in time you will lose the elephant and have to try again.
To win the mini-game you will need to repeatedly press the space bar for 10 seconds. When the 10 seconds are over you need to make sure it is on the “winning” side of the bar at the top. Repeat this process until you are close enough to feed the elephant the peanuts you bought.

<Image from the Official Black Desert Wiki>
Once you have given the elephant the Peanuts, you can now tame the elephant. If you are unsuccessful the baby elephant will kick you and run away. If this happens you will have to start the process again. If you are successful, the baby elephant will start to follow you.
Bring the elephant to the Guild Stable Keeper in Valencia and click on the ‘Register’ button.
The baby elephant will then be exchanged for an item which you can put in the Guild Storage. The item will appear in your inventory and will weigh 800Lt, put it in the Guild Storage nearby.