Trying to set velocity to a gameobject without a rigid body

public void Update (float deltaTime)
{

            //not really sure what the syntax is to set the velocity
	       splash.velocity.Set(0, 0, 0);
}

Your syntax is whack. You should work your way through at least one official Unity tutorial, it’ll answer most basic questions.

public Vector3 velocity;

public void Update() {
  transform.position += velocity * Time.deltaTime;
}

This will teleport the object from point to point, which will actually put it inside other objects if they’re in the way. There is a HUGE amount of discussion on this topic already, please search if you need to solve that particular issue.

So how would I go about starting that?

How would I got about doing that?