The only action you can take while activating your Summoned Stone familiar is to move it, and they only have the single move action durring activation. Activation can occur before or after the Geomancer has taken his/her turn. The summon stone card gives you additional rules and things that you can do with your stone(s). To use the card, you exhaust it, pay one fatigue, and one action. The card also specifically states that only one stone may be granted an attack durring its activation while the card is exhausted.
You may only summon one(1) stone per turn since you have to exhaust the card to use it.
You pay one(1) action, and one(1) fatigue to activate the card.
While the card is exhausted, select one(1) of your summoned stones on the map, durring its activation you may make one attack with it using the Geomancer's weapon. This attack does not grant the bonus surge for being adjacent to an enemy and the stone, as that ability can only be used when the Geomancer is making the attack against a creature that is adjacent to the stone.
In all honesty, there is no reason to ever use the fatigue and action to have your stone make an attack because chances are you making two attacks against that monster will result in more damage because of the bonus surge you would receive. The text does read that you may remove a stone that is already on the map and place a new one, then durring one of the stone's activations you can make an attack. If you really wanted to make an attack with a stone, the only situation that it would be helpful is where the Geomancer does not have LOS to the monster, but the stone does.
The biggest thing to remember is, familiar activation constists of only one(1) move action.
The card supercedes the rules because it adds something new to them. Take a look at Reanimate, the Necromancer skill, it tells you that you can make a move action and an attack action every activation. Just read the text and follow what it tells you. The stones are great for making enemies waste actions on, not you wasting actions on them for the enemy's sake.