Crush the Oreos in a blender or food processor. I use my blender on pulse mode, chop setting, until they are crushed but still have some fairly tiny chunks left, but you could crush them more finely if you prefer. Also, if using a blender, I find it's easiest to crush them in 2 evenly divided batches, in order for them to crush evenly.
Beat the crushed Oreos with the cream cheese until completely combined into a dough-like consistency (note: mixture will be fairly oily/greasy. It's ok, this is how it should be and they will not be like this when they're all done).
Cover and refrigerate the dough for about 20 minutes so it firms up a bit (this makes it easier to form the truffles into a ball shape).
Scoop out truffle dough balls using a small cookie dough scoop (mine is the OXO Good Grips Small Cookie scoop, which holds 2 tsp. and my scoops were slightly oversized), then lightly roll in your hands to form a ball shape.
Place the truffle dough balls on wax paper-lined or parchment paper-lined baking sheets, then stick them in the freezer for about 20 minutes to firm up before dipping. *NOTE: This is a very important step and they need to be frozen, not just refrigerated, in order to get firm enough so they cooperate while dipping them so you end up with nice looking truffles.*
When the truffles are firm enough, leave them in the freezer, line another baking sheet with wax paper or parchment paper and prepare your dipping chocolate. (you will take ~6 out at a time when dipping only, because the dough softens back up fairly quickly at room temperature and again, you need them to be very firm in order to avoid a super frustrating situation when you go to dip them).
To prepare the dipping chocolate, place the chocolate chips and vegetable shortening in a double boiler and heat over medium-low heat, stirring constantly, until the chocolate chips are completely melted (if you want to do a color, see the notes section below). Then place the melted chocolate in a microwavable container that is or resembles a tall mug (this will make your life easier later). *You will only reheat the chocolate in the microwave as needed as you're dipping (once it cools a bit it starts to solidify so it will need to be reheated). However, for the initial melting, it should really be done in a double boiler, especially for white chocolate. I know some people are able to use the microwave and it works but it has never worked for me, even on 50% power in very short bursts. For me, white chocolate always seizes up on me when I use the microwave...so I highly recommend using a double boiler.*
Dip the truffles (for this process, see my Truffle Making/Dipping tips HERE
If you're going to sprinkle on decorations without doing a chocolate drizzle, you must do this right after you place the truffle on the parchment paper after it has been dipped in the chocolate. Otherwise, the chocolate coating hardens and the sprinkles will not stick.
If you want a colored chocolate drizzle, see the notes section below.
When you're done dipping and decorating the truffles, they must be stuck in the refrigerator while still on the parchment-lined baking sheet so the coating can chill before you move them to another container (so the chocolate fully solidifies...otherwise when you try to pick them up you will leave fingerprints in the chocolate coating). Also, if you are taking a long time with dipping/decorating, you want to have more than 1 parchment-lined baking sheet going, so you can stick the truffles in the refrigerator in batches because if you don't stick them in there soon enough after dipping/decorating, the inside of the truffle will start to expand and can cause the side(s) of the truffle to crack and/or cause some of the truffle filling to ooze out.
Once the truffles are all chilled, store them in an air-tight container in the refrigerator. Take out the desired number of truffles for serving about 15-20 minutes prior to serving, as these taste best after sitting out a bit (the inside softens a bit after sitting out).