Simple. Use a 10K pull up and a 10K pull down. Wire the common switch connection to the input. The one end of the switch to +5 and the other end to ground. Then you will read zero, 1203 or about 512 for each of the three positions of the switch.
... and for readers of this thread in the future... don't assume that every SPDT switch will have a "center" position where the common pin is connected to neither of the two "on" positions. Indeed, you may find that some have a center position where the common is connected to BOTH of the "on" positions. Probably unusual, but you just know that Mr Murphy will step in of you depend on there being no "both" position.
You CAN buy SPDT switches which come with a promise that there WILL be a moment between the two "ons" where the common pin is connected to nothing.
Probably not too hard to design your system so that momentary "both" or "neither" states don't matter.