The goal of a surveillance mission is to observe the enemy -without- interfering with his activities. It involves an extensive amount of stealth and maneuvering. According to many, this is the core of reconnaissance patrolling. The ability of a team to pull a surveillance job without any hitch often measure its core ability to perform Recon operations.
In order to be successful in a surveillance mission, the team has to identify enemy forces up to the amount specified by the orders. If the enemy is engaged by the team and neutralized it will not count towards the accomplishment factors of the mission. Ideally not engaging the enemy at all should be the course of action since a contact trumps all fundamental of a stealthy or covert mission.
The best method for a Surveillance mission is to intercept the enemy on the move and be able to observe him. This is usually accomplished while positioning your team in a cache between a point of interest (say the LZ or a tactical infrastructure) and the enemy's starting location (usually unknown). A chache should be able to conceal most of your troops while allowing the individuals within to observe outside and at a fair distance. It should also be a defendable position. Some teams like to deploy some claymores in case of a surprise attack or to cover unattended angles.