Cards with Suspend may be exiled, face up, for its suspend cost, with X time counters on them. During your Upkeep you remove one time counter. When no time counters remain, the spell is cast normally, but without paying its casting cost, if any. If the spell is a Creature it has Haste.
Note: suspending a card is not the same as casting it. The card is cast after the last time counter is removed. Counter spells must be played after the last time counter is removed, before it resolves. Triggered abilities that activate when a card is played, or when a card is cast, activate when the last time counter is removed.