How do I calculate the required value for a pull-up resistor?
Quick Answer:  Experience and experimentation is how you figure out the proper pullup/pulldown value.

Long Answer:  The pullup/down resistor is the R in an RC timing circuit.  The speed that your signal will transition will depend on R (your resistor) and C (the capacitance of that signal).  Often times C is hard to know exactly because it depends on many factors, including how that trace is routed on the PCB.  Since you don't know C, you cannot figure out what R should be.  That's where experience and experimentation come in.

Here are some rules of thumb when guessing at a good pullup/down resistor value:


For most things, 3.3k to 10k ohms works just fine.
For power sensitive circuits, use a higher value.  50k or even 100k ohms can work for many applications (but not all).
For speed sensitive circuits, use a lower value.  1k ohms is quite common, while values as low as 200 ohms are not unheard of.  
Sometimes, like with I2C, the "standard" specifies a specific value to use.  Other times the chips application notes might recommend a value.