Sublets usually are found within a couple of weeks before the actual move-in date. Sublets mean that a tenant is breaking his/her lease. This mostly comes from 1 of 2 reasons:
The apartment has problems.
The tenants cannot stay.
Most landlords do not want a turnover (3 tenants in 3 months) (original, you, & the next) The landlords look for primarily year long leases or extended to the next August 31st. When it gets close to a date where it becomes vacant, they tend to be more flexible about sublets (especially if they feel that the previous tenants are going to have to be chased for lost rent not collected under the remaining lease term.) Sublets must be upon the owner's approval (as it is stated so in almost every lease)
Real Estate Agencies don't tend to advertise them and they take as much time and effort to complete as a 1 year rental. Most will put in the effort if they are told up front you're willing to pay the same realty fee as for a 1 year lease. College bulletin boards, Laundromats, Convenience stores are a great way to find them.
If it's just for the summer, you may also want to try a roommate situation. It's a great way not to have to change all the utilities and the like for a short period of time. In some situations, you may find you don't even need to bring furniture!