Spell Speed refers to how "fast" a card effect is. There are 3 Spell Speeds:
Each Spell Speed can only be countered with one that is greater, or equal. The exception to this is Spell Speed 1, which cannot be used against each other in normal play, unless special situations allow it. See "Simultaneous Effects Go On Chain" for more explanation on this.
Summoning a monster and declaring an attack are actions that do not have a Spell Speed, and therefore cannot be "chained" to. However, if the action in question was the last action to have resolved on the field, you may activate a card in response, which then becomes Chain Link 1. For example, using "Bottomless Trap Hole" when a monster is Summoned, or using "Mirror Force" when your opponent's monster declares an attack, and all considered to be "activated in response".