# you who have kept with your servant David my father, what you promised him

"you who have done what you promised your servant David my father" 

# you spoke with your mouth

"you yourself spoke"

# and have fulfilled it with your hand

"and, by your power, have fulfilled what you said" or "and by your power have done what you said" 

# as it is today

This refers to the day when Solomon was saying this prayer.