Well you definitely need a second game. Unless you're just gonna restart your main town, then having a second game would be unnecessary. If you currently have a digital copy, you can only get a physical copy in order to even have a second town. If you have a physical copy now, well you're all set to buy whichever version you want. Although I'd probably recommend another physical copy since they have sales and mark down prices in stores or on ebay/amazon/etc because it's an older game.
You don't really need a second memory card since that doesn't really go into the process, except when you don't have enough room for both games. It's usually recommended that you don't play and switch SD cards though because of corruption and you might not remember the date when you played one game verses the other. Just complications all around really lol
You can have two towns on one 3ds, so unless you're willing to bring out the big bucks to buy another system, it's not really necessary either. My friend, when she used to play, had two games one on her old 3ds and another on her 3ds xl, so if you have that kind of set up then you're pretty much golden.
To start a cycle town, just get another game/reset your old game. Make a new town and start moving those villagers. I think you need to get 100% rating and everything first before villagers will move out though, I'm not sure on this but I think it's safe to say that you need to just play normally for maybe about a week. Let some new villagers move in and such, and then start the cycling process.
Here's are some pretty good guides.
http://www.belltreeforums.com/showthread.php?152911-Foolproof-Cycling-Method
http://animalcrossingus.tumblr.com/post/83026695759/villager-movement-guide-v1-0
http://www.neoseeker.com/forums/50570/t2090387-villager-cycling-guide/
Remember though that if you do have cycle purely for one town and don't want it to influence the other, TT via the in-game clock and not the 3ds clock. (This is also assuming that you'd only have one 3ds)