For the 3006 the blue wire (port 1) or grey wire (port 2) should be attached to the nmea + in on the st4000. (Not the sea talk). These wires are on the power data cable going to the GPS. The black 12v neg wire needs to Have a jumper connected to the nmea - in on the st4000. Again not the sea talk connection. The attached shows the location of the nmea connections on the back of the st4000 control head (pg66 of manual)

Appropriate communication settings need to be adjusted in the Garmin for either port 1 or port 2 depending on which wire was attached to nmea +. Make sure you use 0183 as 2000 does have many differences. Wiring for ap is on page 6 of Garmin manual.
If the ap is accepting the track and then veering off without an error or off course message I would look for a magnetic/item near the fluxgate compass. I had an issue with this when a tool bag was placed a few feet from the compass on the other side of a bulkhead. Essentially it would start off on course then do a crazy Ivan at various intervals. In addition to looking for metal items make sure it is well away from any wiring - I have heard of more than on ap going crazy when a microwave, stereo or some other device is turned off or on.
Usually the wires would be crimped to appropriate sized spade connectors and pushed on terminals on back of control head. Extension wires would use butt connectors to the Garmin wires if additional length is needed. Spade terminals if I remember are not 1/4 but rather .125 or .118". Can't remember which.
http://www.manualslib.com/manual/313958/Raymarine-Autohelm-St4000.html?page=37#manual
http://busse-yachtshop.de/pdf/garmin-GPSMAP3006C-3010C-InstallationGuide.pdf

Appropriate communication settings need to be adjusted in the Garmin for either port 1 or port 2 depending on which wire was attached to nmea +. Make sure you use 0183 as 2000 does have many differences. Wiring for ap is on page 6 of Garmin manual.
If the ap is accepting the track and then veering off without an error or off course message I would look for a magnetic/item near the fluxgate compass. I had an issue with this when a tool bag was placed a few feet from the compass on the other side of a bulkhead. Essentially it would start off on course then do a crazy Ivan at various intervals. In addition to looking for metal items make sure it is well away from any wiring - I have heard of more than on ap going crazy when a microwave, stereo or some other device is turned off or on.
Usually the wires would be crimped to appropriate sized spade connectors and pushed on terminals on back of control head. Extension wires would use butt connectors to the Garmin wires if additional length is needed. Spade terminals if I remember are not 1/4 but rather .125 or .118". Can't remember which.
http://www.manualslib.com/manual/313958/Raymarine-Autohelm-St4000.html?page=37#manual
http://busse-yachtshop.de/pdf/garmin-GPSMAP3006C-3010C-InstallationGuide.pdf