That's an awfully long question.
If the pickups are truly active, then they will need a voltage supply in order to make any kind of signal. Usually this means a 9V battery. Most EMG pickups are active, as well as the Seymour Duncan "Pro Active" series and many of their 5-string and 6-string soapbars. Aside from these, most other bass pickups are actually passive.
It depends on the pickups, but in almost all cases, an active pickup can be run by itself (with a battery) followed by passive controls, such as volume, tone, and blend. In other words, you don't really need a pre-amp. However, here is the point where you need to do some research, and find out whether (1) the pickups really need voltage, or (2) the pickups are passive but are connected to an active onboard pre-amp which needs voltage.
If there only two conductors coming out of the pickup, then it's got to be passive. Active pickups need at least 3 conductors: ground, signal out, and voltage in. Sometimes the ground and signal out conductors are in a single coaxial cable.
For true active pickups, be aware that you will need a new battery clip as well as a proper "stereo" jack which will complete the circuit only when a mono cable is plugged into the jack.
There are various wiring resources out there, so it shouldn't be too hard to figure out. If you still need help, you should take some pictures of the pickups and whatever was attached to them (and provide the model numbers on the pickups, if possible) and we'll do our best to assist.