How can I find out which leads are +, - and video signal on this miniature camera?
Looking at the back of the camera (connector side):

Positive - connected to the bottom side (anode) of the tube-looking diode just above the connector. This is a common practice to place diodes on the positive terminal to protect device from reversed polarity. There is also a voltage regulator IC nearby which definitely tells that we are looking at power line.

Negative - connected to all mounting holes and to the negative side of smd capacitors above and below the voltage regulator IC. Grey line marks positive terminal on these capacitors unlike the usual round electrolytic caps.

Video out - most probably pin 4 of the connector if counting from top, you will need to check it yourself by connecting to some video input you have around.

Use buzzer mode of your tester to find out exact pins of the connector.