There are no rules for specifically attacking with a shield.

You could model it by using the improvised weapon rules, and say that a shield does 1d4+STR bludgeoning damage. 

In my game, however, a shield bash is covered by the unarmed rules. 

The reason I did this is to separate things you pick up and drop (improvised weapons) from things you wear (gauntlets, boots, helm, shield). 

I rule that unarmed attacks do 1+STR damage for no armour and light armour, 2+STR damage for medium armour and/or shield, 3+STR for heavy armour. I figure that a headbutt or elbow strike while wearing plate should hurt more.

Unarmed strikes (including my rule of shield bashing) are not weapons, so they don't trigger some feats and features.

Note that the game does have a rule called "shield bash". It is not an attack, however,  it is a shove contest granted by the Shield Mastery feat.