Personally, I choose them based on the colour scheme.
You see, resistors have these pretty coloured bands on them, and you have to coordinate them, otherwise they look bad. For example, a 560k resistor is good because it's green, blue, black, orange. Really nice bright colours. But I would never connect it to a 330 ohm resistor, because that's orange, orange, black, black, and that's pretty plain, so they just don't work together.
Seriously, there's no simple answer. Once you understand what the components do, and you know the voltages and currents that should be present in the circuit, you can calculate the appropriate values using various simple formulas; most often, Ohm's Law, for resistors at least, and the capacitive reactance formula, Xc = 1/ (2 pi f C), for capacitors.
Often, a component can have quite a wide range of values and the circuit will still work fine, so I try to reduce the number of different resistor values in the bill of material to simplify sourcing the components.
For example, in a typical CMOS logic circuit, a "pullup" or "pulldown" resistor (resistor that is used to pull a circuit node to a particular state) could really be any value from 1k to 100k, and it's conventional to use a standard value such as 10k. But if the same circuit also needed an 8.2k resistor for a different part of the circuit, and didn't need any resistors of "exactly" 10k, I might use 8.2k resistors for my pullups and pulldowns, to reduce the number of lines in the BOM.
Resistors are manufactured over a wide range of values - ten orders of magnitude and wider - and very low and very high values are needed for specific types of functions. Exact values are also needed to set exact voltages and gains in circuits. But often, values are not critical, provided they're in the right ballpark.
If you have a specific circuit you're interested in, post it, and we can talk about how you choose suitable values for the resistors and capacitors.