What are Arachin ערכין and how does one figure out their value? In a similar vein, what are Nedarim נדרים and how are they figured out? And finally, what is the difference between these two items?
Erechin are described in Leviticus 27:1-8, and the idea behind them is discussed more here. The Torah assigns a simple "erech-value" to people based on their age and gender. Thus if someone pledged to donate "the erech of so-and-so", s/he would look up their age and gender in the erech table and be obligated to give that amount of silver.
A neder means a person vowed to bring a sacrifice. (See Rashi, Leviticus 22:18). So if a person said they hereby made a neder to bring, let's say, a shelamim sacrifice, s/he would be obligated to bring some appropriate animal as a sacrifice.