To basically summarize and re-organize the linked-to answers:
1) When a charge $q$ is moving (say at velocity v) through a perfect conductor such as an ideal wire, it requires no force to maintain its velocity because it encounters no resistance. This is good, since there can be no electric field inside a perfect conduct and thus no force can be applied to the charge by the electric field.
2) Resistors are not perfect conductors. When you think of a resistor think of a thick line of graphite, which is partially conducting but certainly not perfectly conducting. Indeed, you can create your own resistors with a pencil and paper by drawing a very thick heavy line on the paper (you can check the resistance with a voltmeter).
3) Because resistors are not perfect conductors there is a "resistive" force (say, $-\alpha v$) on the charge and thus it requires a force on the charge to keep it moving along. This force must be applied by an electric field which has built up within the resistor, which requires a drop in voltage when passing through the resistor of IR (it is linear in the current because the resistive force is linear in the velocity).
So, in your example, the fact that the battery is 9 volts means that the battery is saying "I will do $9q$ work on each charge to get it through the loop". But, for example, if there is only one resistor R, the battery only needs to do $\alpha v L$ work on the charge, where L is the length of the resistive segment. Thus, the velocity of the charge in the loop will adjust to make the work come out right. I.e., the current (which is $qnv$) will adjust to become I=V/R.
