DC Circuits are circuits where the charge always moves in one direction. Commonly we assume charge moves from the positive to negative end of a field (or more simply the positive end of a battery to the negative end of a battery - or EMF). Charges carry electric potential, or what is also called voltage... which is like potential to make stuff happen. All voltage must be use in the circuit before charge can return to the battery (ie you can't have any potential to do stuff left. See Khirchhoffs Rules.) Charges will move more or less quickly (Current) based on the resistance (sort of like friction) in a circuit. The more resistance, the less charge can flow. The flow of charges is called current, which is defined as Q/t (an amount of charge moving past a spot per second).
Any resistor can use up that potential we just mentioned above. The voltage used in any resistor is subject to Ohms Law (V=IR) of the voltage used by any resistor depends on the size of the resistor and the current that runs through it. The wires in a circuit inherently have resistivity. Which depends on the size of the wire (length and area) and material it is made out of. If the wire has a greater area, charge the more easily charge can flow without being impeded (an inverse relationship), the longer a wire is the more it will be slowed (a direct relationship). Some materials are more resistive to flow than others, based on the their properties. Resistance of a wire is R = rho(l/A) where rho is the resistivity property of the material.
There are four types of circuits to look at: simple, series, parallel and complex.
~A simple circuit uses one emf and one resistor on one loop. The addition of more loops with no resistors creates a "short" that allows current to flow unimpeded. This can lead to high current which causes wires to heat up from the friction of fast moving charges in the wires and can lead to fires.
~The series circuit is one wire with two or more resistors inserted one after another. Current must flow the same through all of them because its like a single lane road, there is no deviation. Resistors will share voltage based on the size of the resistor (since current is the same through all of them). The total current going through a series circuit depends on how many resistors stack up along the wire.
~A parallel circuit allows charge do move down two or more branches so it can run parallel to other current at the same time. The amount of current splitting to each branch depends on the resistance down each individual branch and the voltage available. The voltage down parallel branches is the same because the voltage available in the charges of each branch are the same before they split down each branch. The current coming from the battery is the sum of the currents in each branch.
~A complex circuit will have a series with a parallel and possibly more than one battery. Using ohms law repeatedly becomes more difficult and Khirchhoffs Rules are much more applicable and useful tools.
Its helpful to think of a circuit as a bunch of connected pipes with water flowing. The battery or EMF pumps out charge like a water pump. You can't really change the size of your pump, so it is helpful to think of ohms law not as V=IR but I=V/R... where current is the result of how much your pump can push out water and how much resistance there is to that flow. Resistors are like screens and filters in the pipes that slow water down and take away some of its kinetic energy. The current in circuits can vary based on the type of circuit. A series circuit is made of only one continuous pipe so current has to be the same everywhere. A parallel circuit offers alternate routes for the water to flow in more than one pipe so the flow can split up. The total flow of water out of the pump is equal to the total flow in all parallel pipes.
Loop Rule (Voltage Law): Conservation of Energy - The sum of the voltages in a loop of a circuit is equal to 0.
Junction Rule (Current Law): Conservation of Charge - the sum of the charges (current) entering and leaving junction (3 directions minimum) is equal to 0.