~  Final Fantasy IX  ~ 
Summon beasts in FF9 can only be called on by those of the Summoner tribes born with them. Summoners can also trade or have their summoning powers (gems) extracted from themselves. Shiva in particular can only be used by Garnet who was born with the ability. After Queen Brahne dies, Dr. Tot returns Shiva and a few other summons (that were forcibly extracted) to Garnet. Then, once you have an Opal equipped on Garnet, she can use Shiva. After 20AP is gained with it on, she can use Shiva without an Opal equipped.

In case you're wondering, opals look like this. Still, opals come in lots of variety but always have shards of color, like ice! There's one even called a water opal. Opals in FF9 can be used as items in battle too, they restore 1000 HP. Vivi can also learn Blizzara from equipping an Opal.

Shiva looks very regal and strict in this game, with her icy crown and jewellry but her facial features still remain Indian looking (including bindi). I think the regal touch has to do with Shiva's origins for this game (read below) and Garnet's royalty culture.

Madain Sari Wall
In Madain Sari you can see a depiction on the wall of a small girl, who is Shiva. It's a young girl because Shiva takes many forms. She has a bindi on her forehead and her legs are crossed, just like older FF Shiva summons and the actual depictions of Lord Shiva of the Hindu religion. The text on the wall follows.

The First Eidolon Discovered, Shiva:
Shiva took the form of a young girl when she was first discovered. She now appears as a grown woman.
Eidolons adapt their forms to the time and culture in which they appear. Shiva illustrates this theory.
In certain areas, Shiva is depicted as a snow fairy. This cannot be verified, since the only written document that remains is in the summoner village.
People associate Shiva with the snow fairy.
Why she changes forms remains a mystery.

Shiva's only attack is Diamond Dust, a powerful Ice-Elemental attack on all enemies. It costs 24 MP to use and can be done as many times as you like. It does most damage on Fire-Elemental enemies, up to 9999 on them. Her max damage on non-Fire enemies is 7000. The more you summon Shiva, the more damage she does.

Normal & Short Animation
Since the complaints of FF8's overly long GF sequences, in FF9 the first time you use a summon, you see their full intro and attack. From then on, you only see their attack. To get the long animation again you must use the Boost ability.

With the boost ability learnt and/or on, Garnet can boost Shiva's damage during battle. It works like FF8's boost in that you have to watch the full summon animation and boost during it. You also can boost Shiva's damage by having a lot of Opals in your inventory. To get more Opals you can synth them at Daguerreo's or the Black Mage Village's Synthesis Shops (Ores + Potions).

Quad Mist Card
You can get more than one Shiva card. The easiest is by ringing the bell at Alexandria (at the beginning of game and at Disc 3). Aside from that, win it from Summon/Eidolon Master Leyra or Straight Shooter Shak at Treno Card Stadium.

Quad Mist became Tetra Master, the Shoukan (Summons) command became Eidolon and Shoukan Kedamono (Summon Beast) became Eidolon. Another word in FF9 JP for Eidolon was Yuurei meaning phantom. Eidolon actually means phantom or image/ideal too.