The attack must be made by something capable of grasping or netting the stone
Thereafter, another creature must use an action to grasp or net the stone to separate it from you, either by making a successful attack roll against AC 24 or a successful DC 24 Dexterity (Acrobatics) check.
The only way to separate the stone from its owner (without destroying it) is to "grasp or net" it. While "net" has multiple meanings as a verb, by far the most common and most relevant in this context is the obvious: to catch something in a net.1 So, hitting the stone with any attack capable of grasping or netting it will do so. Hitting with any other attack will have that attack's normal effects (typically dealing damage to the stone).
So, what kinds of attacks fulfill this requirement? Certainly an attack with a net qualifies. You could make an argument that an unarmed strike with a free hand could grasp the stone, but I think the more reasonable ruling in that case is for the DM to treat it as a Dexterity (Acrobatics) check rather than an attack roll.
Arguably, any attack that can target objects and that inflicts the grappled or restrained conditions on a hit should also be eligible to grasp or net the stone. Although conditions, including grappled and restrained, are only meaningful for creatures, the fact that an attack inflicts one of these conditions indicates that it is an attack capable of grabbing or grasping. (Note that an attack with a net also fulfills this criterion.) For example, a giant crab's claw attack is made against "one target", so it could grasp the stone by attacking it, though with only a +3 modifier, it will need a natural 20 to succeed (and it will deal damage for a critical hit in addition to grabbing the stone). However, a constrictor snake's constrict attack targets "one creature", and hence cannot grasp the stone.
Conversely, attacks capable of causing forced movement should probably not be able to separate the stone from its wielder, since pushing or pulling is not the same as grasping or netting. Also, effects that involve a saving throw or ability check instead of an attack roll cannot affect the stone, with the sole exception of a Dexterity (Acrobatics) check.
Ultimately, it's up to the DM to decide which attacks are capable of grasping or netting the stone. A net attack and a sword attack are easy cases to decide, but a pincer claw, a bite attack, a tentacle grab, a roper tendril, etc. are more ambiguous cases not clearly spelled out in the rules, which means we fall back on the 5e principle of empowering the DM to fill in the gaps.
1The more general, figurative use of "net" as a synonym for "acquire" is almost exclusively reserved for financial and figurative contexts and is typically used with a different syntax, e.g. "selling my Ioun stone netted me 5000 pp". This definition is almost never used in reference to physical objects, and is almost certainly not the intended interpretation in the context of taking physical possession of an object.