Transformers are wired to the track with the hot wire to the center rail, and the neutral (or ground) wire to either outside rail, usually the rail closest to you when you are facing the layout.

Accessories that stay on all the time, like lights, get both power and ground directly from the transformer accessory terminals, no track connections needed.

Accessories that you wish to have a train activate need the Accessory Activating Track. The hot wire from the accessory terminal of the transformer gets connected to the accessory directly. The ground accessory terminal gets connected to the same rail as the ground from the track portion of the transformer. They are connected together. The ground wire of the accessory gets connected to the insulated outside rail of the Accessory Activation Track. When the train rolls onto the insulated track section, its wheels bridge the live outside ground rail with the insulated rail, completing the electrical path to the accessory, and activating it. When the train passes, the circuit is broken, and the accessory turns off. Here is the owners' manual for the Accessory Activation Track; it shows the electrical hookup.

The special track sections get placed anywhere on the layout that you wish to activate the accessory.

Larry

Giving specifics on the accessory you are trying to wire will help.  There are options and a few different methods depending on what the accessory does and how you would like it to function.

Does the accessory do one thing (like just light up) or does it do more (like light up and also have a man come out of a building).

These details can alter how you may wish to hook it up.  For the power, you do not need to wire it to the transformer and the track, one will do.  Transformer is preferred by many since the accessory posts will provide the same voltage no matter how fast you have the train set to go - if you hook to the track, the accessory voltage varies with the engine voltage, and the accessory may not work  (and won't work at all if the train is stopped).

As to track, general convention is for "hot" to go to middle rail, "common" (many also call it "ground") to the outside rails (which are connected together for a standard piece of FasTrack)

See above.  Except for a special case of wanting to trigger the accessory action when the train goes by (see below), you would not normally hook to both the transformer and the track.  Walk before running...

You need a special insulated track setup to do this.  For FasTrack it's referred to as "Accessory Activation Pack" (or something close to that).  It's called insulated because one of the outside rails is not connected to the other.  (and there is a gap in the rail on each end of this insulted rail as well so it does not get connected by the next piece of track on either side(which do have their outer rails connected).  This allows the wheels of the train to complete the circuit to activate the accessory.  This is useful for gateman and switch towers where you may want the man to come out when the train goes by.

-Dave

There are a number of good resources to read in the resource library for this forum. When i got started this book by Riddle was very valuable too.

Hmmn, enter the new Plug n Play accessories...

yes, can you use Lionel part numbers for the accessory and the track section.

Generally, the outside rail is just that (2 of them) and used for common or U. The third or center rail is hot or A.

When using a common rail (outside rail) as an activator rail, it doesn't matter which one is used, only that the isolation(insulated) is on the same side.

 I believe it is straight forward if you look at the instruction manual and then watch Mike Reagan in the Lionel videos.

Please provide the accessory and track parts number and we'll get you through it. It's always a good idea to be specific about which item(s) you have when discussing a problem or requesting assistance with any issue on the forum. You will quickly get concise replies.

Letting us know exactly what you have is a must, pictures, age and/or numbers help too. List these and then the possibilities about what can be done with it will flow. But all sounds right so far. Placing the Acc. track may require some test and tune. Remember the wheels are your switches for isolated rails, so move it where it turns on when needed. Extending and/or creating your own isolated tracks isn't hard, (use OGF search, find threads) When buying don't be afraid to do some research, and ask some questions here first. Here's some common carp or...well lets just see what floats, and what sticks... Make sure items are for AC voltage and can handle 18v-20v peaks without damage(to 24v for pre war transformers). Most Lionel items will be fine +90% of the time, but even some of the 1970s-80s Lionel items used DC voltage. Don't use any DC items with the AC transformers without adding a bridge rectifier (about $5) to change AC to DC. With a rectifier and a small regulator (or just a wall wart) power to battery operated goodies can be supplied. LED lights use DCV, regular light bulbs don't care and can use acv(ac) or dcv(dc). Depending on the accessory you may want to check into using what I bet is the most popular little orangey red button of all time, The Lionel #90. (Id hold out for one with the "L" on the button)

A Lionel loco will run either way its wired to the "variable posts", but...a quick way to tell if your wires are correct is blow the whistle/horn if you have one. If it doesn't work, or if loco is bell equipped and you hold whistle/horn two seconds but the bell rings, you need to reverse the leads. (or if the bell button blows the horn, switch the leads). Because its transformer AC, your track doesn't really have a "positive" "negative", or "ground". Those positions kind of change as the AC goes from positive to negative and back 60 times in a second (60hz) The "variable" power legs should always go to the center(middle) rail and the "common(s)" goes to the 2 outside rails. Black is "common" on your CW-80. Common to both fixed and variable circuits, because the two black posts are connected inside. I suppose you could call the non-common(red) fixed voltage "constant", or maybe "hot". We get "lazy" and refer to "common" as "ground" and use other "slightly incorrect" terms often. Equipment changes the lingo too. Just keep that in mind and don't be afraid to ask. Some other transformers in the past (post war era or "PW"  used a variable common so if using (and phasing) two old transformers together, one may lose use of a whistle control, but might gain a bell control. Ie the U post("universal") is not always the "common" and might, or might not be "variable". Old PW whistles often need a 5volt boost to start well too. This boost was present in much old equipment, but the boost is not available in many modern transformers. The horn/whistle/bell relays old and modern are activated by a 1.5 volt dc current sent right along side the ac track power. Its a "positive dc offset" for whistles/horns. If you saw the just ac power as waves like on a oscilloscope, the peaks(+pos.) and valleys(-neg) would be equal distances from zero. If peaks are farther from zero(middle) than valleys that's a "positive offset". If the "valleys" are deeper from zero/center than the "peaks" are tall, it is a "negative offset" so the bell rings instead, if your loco even has one. Not all transformers, or trains have whistles/horns(or smoke). Even less of both have had a bell. 

Here is a link to resource material that may be helpful with your adventure.  Click on the underline phrase to link. 

Best wishes with your project

Mike CT

Kalmbach Bookstore

Essential series

Basic Wiring for Model Railroaders

This forum is a great place to get information about your trains or help when you have a problem. However, if you are just starting out the best thing you can do is get a good book on wiring your train and layout items. This may not answer all your questions, but will give you a good understanding of how it all goes together. Here is one that helped me out a couple years ago. I had another book prior to this, but for me this one was more informative, easier to understand, and easier to read. It's also for 3 rail AC O gauge trains, which is a little different (also a bit easier) than the 2 rail wiring for DC. Good to know about 2 rail and DC also, but you can get to that later.

Here is a link to the book on Amazon: Wiring Your Toy Train Layout by Peter Riddle 

Your local hobby shop (if you have one) may also have it and is another good place to ask questions about your purchases. They can help you with all the things they sell, or at least they should be able to. 

A Classic Wiring Book • from Kalmbach Publishing • by Ray Plummer

Lots of pictures of book covers in this thread.

If you want a Lionel manual that describes and illustrates exactly the wiring your asking about go to this thread ' Electrical reference materials and manuals'  in this forum (electrical).

Scroll down to the post that includes the 1954 "How to Operate Lionel Trains and Accessories".

That is the manual you want.  Download it.

Direct link to the Lionel manual here.

Larry