What you need:
1. At least two characters sharing the same level.
2. A Manipulate materia
3. A Transform materia/ a means to shrink characters
4. 1 or better 2 Enemy Skill materia with Goblin Punch
5. Possibly HP+ materia (if anyone's maximum HP is below 777)
Simply follow these steps:
1. Choose a team of 3 characters, at least two of whom share the same level, whom you intend to enter the Lucky 7s status.
2. Give the Manipulate materia to the character who shares his/her level with another character in your team.
3. Give the Enemy Skill materia and the Transform materia to the characters without the Manipulate materia.
4. Unequip accessories preventing the Mini status.
5. Lower all your characters HP to a value below 7777.
6. Enter a battle against some enemies, at least one of them being susceptible to Manipulation.
7. Defeat all but one enemy, manipulate the remaining enemy.
8. Cast Mini on the two of your characters who are not manipulating the enemy.
9. Use Goblin Punch to lower all of your characters' last two HP digits to 77, 78, 79, 80, 81, 82, 83 or 84. ***
10. Use the normal attack command to lower all characters' last two HP digits to 77.
11. Flee from the battle or defeat the enemy.
12. Use Hi-Potions and Potions on all your characters until their HP are at 7777 or below.
If you increase your HP to 7777, you will start the next fight in the Lucky 7s status.
If you increase you HP just below 7777 (7677 for instance), you can manually cause the Lucky 7s status in the course of the next battle by using a Potion/Hi-Potion.
Note that while being afflicted with the Minis status all physical attacks of that character deal exactly 1 HP damage. Yet, Goblin Punch bypasses this rule: If a shrunken character uses Goblin Punch on someone (friend or foe) who shares the same level with the character using Goblin Punch, the damage will be multiplied by 8. Thus, if Vincent (Lv. 85) in Mini status uses Goblin Punch on Cloud (Lv. 85) or on himself, Vincent will inflict exactly 8 HP damage.