Your opamp circuit has two identical channels. So you can analysis only one channel. And you can brake the circuit into the functional blocks quite easily.
Jony has the right idea, regarding a functional block breakdown of the circuit.
From a high-level view, a function block is just what it sounds like.... a "black box" that takes some inputs, and generates some know outputs, based on the inputs. Think back to your grade school math class, when you first learned about math functions. A function f(x), takes a variable, x, manipulates it, and returns that value. Example:
If f(x) = 2x+3,
Evaluate the following.... f(x)^2 - 5*f(x), when x=3
How do you go about solving it? You plug 3 in for x, evaluate the FUNCTIONAL BLOCK of math that is f(x), then stick it's output into the top-level equation, and finish evaluating. Like so:
f(3)=2*3+3... so f(3)=9, then
9^2 - 5*9 = 81 - 45 = 36
The same can be done for any complex system, from hydraulics, to biological process, to chemical reaction, nuclear power plant cooling systems, and even electronic circuits. So, like Jony showed, find a part of the circuit that looks like a common, well-known circuit and make a perimeter around it. Some signals come it, that well-known circuit performs a known task (amplifier, filter, inverter, etc), and supplies some defined output to the next item in the system. Once you've seen some of the standard circuits a few times, they will become easier and easier to identify.
It takes time to deconstruct complex circuits, so take your time, and pick through them one bit at a time. Look for circuits that you know, and then grow out and follow the signal flow from there. It takes practice, but sooner than you realize, you'll be ripping into complex circuits without any fear or hesitation.
When all else fails, you can always fire up PSPICE (or your favorite circuit simulator), build up a
small part of the circuit, run some signals into it, and see what comes out the other side.