Costa Rica has no millitary, all armed forces were permanently terminated in 1948. This termination was turned to law in 1949, when the new constitution went into effect. Currently there are no defense forces of any type, aside from the police and it's different units, and no required service of any type for citizens.
The country prides itself as a neutral state, and works on the premise that if they don't bother anyone, they won't be bothered. This has worked well for the moment, and no serious conflicts have ocurred, even during the nicaraguan uprising of the 80's and the invasion of Panama in the 90's.
International conflicts which may have warranted millitary action (i.e. Isla Calero, 2010 ) are normally handled via diplomatic channels and local police. In the case of Isla Calero, the area was put under watch by civillian police, and a formal complaint was filed against Nicaragua in the International Court of Justice in the Hague. No armed conflict or combat ocurred, as far as is known.
Despite the neutral image Costa Rica projects, it has been involved in some contemporary millitary operations. During the Nicaraguan crisis of the 1980's, the northern part of the country was home to several millitary bases and anti-aircraft stations. It's rumored that the highways in the north were originally designed as runways for C130 aircraft. Though most versions of these millitary operations in CR are said to be urban legend, you'll find many locals up north and in the different police forces, that will assure you they saw and even operated at the bases in the 80s.
Aside from the 1980's, Costa Rica is currently involved in several agreements with the United States which allow millitary vessels to navigate territorial waters, and resupply at the ports. These agreements seek to control drug trade, intercepting shipments from Colombia and Venezuela that are headed towards Mexico or the US.
Millitary support is provided, if needed, through international agreements, mainly by the United States. Help is usually dispatched through the US Southern Command (USSOUTHCOM) which operates out of Florida and has a base in Honduras. On occasion, millitary aircraft will be seen flying over the country, on their way to or from the USSOUTHCOM base.
Internally, order is maintained by civillian police forces, which have specialized units for riot control and SWAT operations.