Ohm's law (which should be familiar) is a very useful rule. Note that it only applies to resistive loads however. The impedance of other passive components may vary with (e.g.) frequency (e.g. capacitors) and many components do not obey this rule at all (diodes, transistors etc.).
Resistance determines how much charge flows per second when a voltage is applied. Resistance is lower if the material the device is made from has many charges (normally electrons) init and if the charges can move easily through the material. Both of these depend on temperature.
Kirchoff's law, which is common sense, states that the sum of currents at a join in wires is always zero, i.e. any charge (current is a flow of charge) which goes in must come out somewhere.
V = I x R
This is only true for resistive loads. Most loads are more complex than this.
V = I x Z where Z is the impedance of the load.
This may depend (forexample) on the frequency of an A.C. signal.
Kirchhoff's Current law
What goes in, comes out.
A simple application:
There is a tacit assumption here that no current flows in the output