From what I understand about OBD II swaps, you need a '96+ LS swap. You cannot use the engine wiring harness attached to the B18B as the '96+ Civics use a completely different harness. EG ('92-'95 Civic's) and DC ('94-'00 Integra's) use a 2 piece harness. One that attaches to the engine and one that stays in the car. In '96, the EK Civic's ('96-'00, although there are some differences between the '96-'98 and '99-'00 Civics) changed to a complete 1 piece harness that attaches to the engine and then goes through the firewall and directly to the ECU. It completely comes out with the engine. Good news is, the engine side of the harnesses are basically the same (some sensors may be different locations and such, but they're pretty close). You can strip your old engine of it's harness and use it on the B18B. I believe (I haven't done my '98 EX's swap yet) that a '96-'98 ECU will plug into a '96-'98 ECU harness (and so on for the '99-'00, that's the major difference is the shape of the ECU plugs).

You'll also need the complete normal swap kit. Axles, shift linkage, mounts (I'm not sure specifically which mounts though), the complete engine/sensor/tranny/manifolds combo and the proper ECU. I think for mounts you need the '99+ Si rear mount and a B-series front lower tranny mount and front lower engine mount. The other 2 can reuse your Civic pieces. Like I said, I haven't done my swap yet (probably another month or so, I'm planning to post each step as I do it) but this is what I've heard. Aside from the normal swap headaches (axle nuts, shift linkage pin ...) the swap is pretty easy.

I would definately recommend you purchase a Helm's manual for your car and also one for the car your engine comes from (IE a '97 Civic and a '98 Integra if that's what you get). Each book contains a 15 page or so section on how to remove and install and engine, with pictures, torque valves and any special tools you need. It's extremely helpful and will give you a good starting point on the mechanical aspect of it all. They're about $66 a piece shiped (at least a year or two ago) but worth their weight in gold.

http://www.helminc.com/helm/homepage.asp?r=

They're the factory service manuals used by OEM techs. Just call them up with your credit card and at least get your Civic's one. Good luck and let us know how it goes.