My US History teacher recently mentioned an uncertified story which basically said that when the CIA was spying on Cuban military bases, they noticed that they built a new soccer field, which was strange because Russians played soccer not Cubans. The CIA became knew something was up, and quickly noticed the construction of the missile sites.
Is this at all true? And if so is there a picture?
Two different situations. Large movements of Soviet personnel and equipment plus the installation of air defenses in 1962 prompted US suspicions that the Soviets were building a ballistic missile base. There is a good contemporary summary of the intelligence leading up to the crisis on page 34 of this collection of CIA documents.
The soccer field incident was in 1970, when discovery of the fields supported the conclusion that the Soviets were building a submarine base in Cuba. Kissinger confronted the Soviets privately and they provided assurances they would not build a base. The Soviets still periodically had a naval presence in the region through the '70s and '80s.