Dc puts the power to the track from you power pack/throttle and the locomotive picks up the power directly from the track. The newer power packs since the 80s or maybe even into the 70s use transistor controlled throttles to modulate the voltage, lower voltage = lower speed, higher voltage = higher speed. If 2 or more locomotives will run at a reasonably close speed you can run them together on dc. Unless you have your layout wired into blocks, and have separate throttles, you can only run one train at a time. If you have it wired into separate blocks that are isolated from one another, and either have a separate throttle for each block and move from throttle to throttle as your train moves around the layout, or have rotary switches that will direct each block in turn to one or the other throttle, then you can run more than one train at the same time. My experience with trying to run multiple trains is that one train is enough for me to keep track of. It is one of the advantages of being in a club or having some model railroad buddies to come over and operate trains. That is a "down & dirty" description of dc.
With dcc, a constant 14 volts is supplied to all of the tracks all of the time. There is a decoder inside the locomotive. You put the locomotive on some sort of programming track and assign an address to the decoder in a specific locomotive. The dcc system sends a high frequency digital ac signal through the tracks. You would have a throttle that will also program. The most common way to address a locomotive is with the number of the locomotive. Let's say you have a model of a Santa Fe Gp40x. From Athearn it will come with #3802 or #3808. For the sake of the example we'll say your locomotive is #3802, and you programmed the locomotive decoder to recognise #3802 as it's address. That locomotive will sit on the track with 14 volts going to it, the light will be lit, but it won't move until you pick up a throttle and tell it to control 3802. Now if you push the forward button on the throttle and turn the dial to power up the locomotive, that throttle will wake up #3802 and tell it to start moving forward, and 3802 will start moving.
If #4556 is sitting on the track 5 feet in front of #3802, but it hasn't been commanded to move, #3802 could run into it just like the prototype. You are no longer restricted to running one train per block. In the modular club that I belong to, we used to run dc control, and the layout would be divided into 8 blocks, for on the inside main and 4 on the outside main. We could run a maximum of 4 trains at one time. If the locomotives of two trains got int the same block simultaneously, both would slow down, but one would usually be faster. If the faster train was in front, we could just wait for it to clear the block without a problem; but usually the only reason 2 trains got into the same block was that one was overtaking the other. When the faster train was in the rear, the only way to avoid a rear end collision was to stop both trains. Reverse both trains until the faster train had backed clear of the block. Then stop that train in the previous block and run the other train forward until the space between them was restored. Now with dcc, we don't have to worry about spacing, relative train speeds or anything. We do need to pay attention to what we are doing so we don't run into the back of another train, but if there is room on the mainline to fit a train, we can bring it out and run it there. We are building a yard for the layout now. When it is completed, with dcc, we can have two switchers working independently of each other in the same yard at the same time. You just can't do that with dc. Dcc requires a starter set that will consist of a power supply, a command station, throttles (either tethered or wireless), and decoders in each locomotive. Thanks to the NMRA setting standards for dcc, decoders are universal. All decoders will work witrh any dcc system. The rest of the system is not compatible, that is you can't use a North Coast Engineering throttle with a Digitrax command station and an Ezdcc power supply. If you buy dcc, get one system. For decoders, you can use whatever the locomotive manufacturer put in, or whatever fits.
When you go to Arnie's in June, ask them to demonstrate dcc and ask any questions you have. I haven't been to Arnies in a long time, but I think they do a lot with dcc.
I'd also like to invite you to come see the Orange County Module Railroaders at the National Orange Show in San Bernardino. We are setting up on Wednesday May 24, and will be operating through the Memorial Day weekend. I'll be there Wed & Thur and I'm sure that whoever is there when you come by will be glad to talk with you and answer any questions you might have. If you want to check us out a bit
www.trainweb.org/ocmr/
