Actually, you get your first +50 Ex Lvl Cap after you complete Stage 4, if I remember well (that means 16 sub-stages).
Besides that, some One-Time Missions will raise that cap by another +5 Lvls, most of them are from the "Reach Lvl X" kind.

I'll search the JP wiki for them and I'll update this.

Originally Posted by chillinfar

After 21 Peronamin: MY HOPE WILL NEVER DIEEEEEEEEEE! Ex card quest completed.

Now how i can use it? I have 3 cards on lvl 100 (2 SR and 1 N) but no option is available.

Now, to answer the OP's question:
The Ex Wild Card works the exact same way as any other WC in the game.
After you get your Ex Levels unlocked, your new Max Lvl for any card will become your Ex Lvl Cap, instead of 100.
The other WCs (N, R, SR, SR3, SR5) will only raise the card's level up to 100. This is when you start using Ex WCs.

Also, of note, is that Gacha rewards will increase you card's lvls above 100 if you have Ex Lvls unlocked.

Don't forget, also, that if you get a gacha reward of a certain rarity, and you have no cards of that rarity left that aren't max leveled, the reward will become the appropriate WC.

- - - Updated - - -

Here it is:

Additional rewards for Special Missions

All these missions give +5 to the Ex Lvl Cap.
The ones in red unlock Ex Lvls if they're still locked, and give +25 instead if they do so.

• Rescue Girls From The Naked King - Clear all Stage 4
• Rescue Girls From The Naked King - Clear all Stage 5
• Rescue Girls From The Naked King - Clear all Stage 6
• Achieve Levels - Reach Lv50
• Achieve Levels - Reach Lv100
• Achieve Levels - Reach Lv150
• Achieve Levels - Reach Lv200
• Raise SED - 1,000,000
• Raise SED - 2,000,000
• Raise SED - 3,000,000

JP max Ex Lvl is currently capped at +70 Lvls.