As written, Judo Throw has two mechanics in GURPS. One is attack-based, the other Quick Contest-based. Not liking two systems for one thing, this is how I've been running this in my DF game:
Offensive Judo Throw
Two attacks are needed:
1) Grapple successfully.
2) Attack to throw. If you hit, and the opponent fails to defend (with any legal defense), your opponent falls.
Defensive Judo Throw
One Parry and one attack is needed:
1) Parry using Judo.
2) Step into close combat and Attack to throw. If you hit, and the opponent fails to defend (with any legal defense), your opponent falls.
And that's it. Essentially, if you have contact with a foe from a parry or your own grapple, you can attempt a throw. It's always an attack. Any defense is valid, but generally if you have grappled a foe you've restricted a lot of defense options (Shields are a liability in close combat, Parry is an issue in close combat for many weapons, you can't Retreat while grappled, etc.) Offensive throws are, in practice, a little easier because you've stepped in close combat already and grappled, nullifying most defenses or at least limited them.
But that's it - one method for both throws.