How to learn how to simplify schematics
Practice. The answer is practice.

The more familiar you become with electrical circuits, the easier it becomes to recognize if components are connected in series, parallel, as a ladder network, etc just by looking at the circuit. There is no rule of thumb to tell you this, it requires your instinct, which is best developed over time. Don't stress over it too much, just take it as it comes and do your best. 

Personally, I usually start from one side and work my way in the opposite direction, simplifying as I go. It may take two or three iterations to make it as simple as possible, so patience is also key.

To start with the circuit you posted, I suggest first looking at the ground node (coming off the negative side of the battery) and make it into just a straight line. Then draw every resistor connected to the ground node vertically, and connect the corresponding end to this straight line. Finally connect the top sides of each resistor wherever it needs to go (trace the connections in your original schematic). At first glance I also see a couple of resistors that are simply short-circuited, so they can be replaced with just a wire.